What are some backgrounds and references to obsolete simplified Chinese characters? During the 20th century, two Chinese simplifications succeeded: the one in China, and the one in Japanese. There were also many abandoned attempts to simplify Chinese , including:


First Batch Simplified Characters (教育部公布 第一批简体字表), not to be confused with the standard simplified Chinese currently used in China;
Singapore Simplified Characters (新加坡简体字); and
Second Stage Simplified Characters (第二次汉字简化方案).


Explain their backgrounds and provide a reference.

(This will be self-answered)
(Warning: long answer)
This Proposal to Encode Obsolete Simplified Chinese Characters is an excellent reference to the different obsolete Chinese simplification standards, although the encoding is yet to be seen :) This answer is a synopsis of the backgrounds provided.
First Batch Simplified Characters (1935) (教育部公布 第一批简体字表)
(From Page 3 of the Proposal)

In January 1934 at the 29th meeting of the Preparatory Committee for the Unification of the National Language (Guóyǔ Tǒngyī Chóubèi Wěiyuánhuì 國語統一籌備委員會) of the Ministry of Education, Qián Xuántóng 錢玄同 (1887–1939) submitted a draft table of simplified characters (Sōucǎi gùyǒu ér jiào shìyòng de jiǎntǐzì àn 搜採固有而較適用的簡體字 案). These were approved by the committee, and Qián Xuántóng was delegated to edit a table of simplified characters for publication. In August 1935 the Ministry of Eductaion published a first batch of 324 simplified characters (see Appendices A and F), with the intention of publishing a series of further batches of simplified characters. However, in February 1936 the Ministry of Education issued a directive halting the simplification program, and no further batches of simplified characters were issued. Although this first batch of simplified characters was not widely used, it was historically very important as it represented the first centralized attempt to promote the use of simplified characters in China, and was a precursor to the simplification movement of the 1950s and 1960s in the People’s Republic of China.
The simplifications in this table were based on commonly used vulgar form characters (e.g. 宝 for 寶), ancient forms of characters (e.g. 无 for 無) and cursive form characters (e.g. 为 for 為). Most of the 324 first batch simplifications are identical to modern standard simplified characters or Japanese simplified characters, but some are different to a greater or lesser extent; and those characters that are not currently encoded need to be encoded in order for scholars to discuss this pioneering episode in the history of Chinese character simplification. Moreover, some of the currently unencoded “first batch” characters are commonly found in early printed texts (see Fig. 1), so it would also be useful to encode these characters for scholars of such texts.


Singapore Simplified Characters (1969) (新加坡简体字)
(From Page 17 of the Proposal)

In 1969 the Ministry of Education of Singapore issued a table of 502 simplified Chinese characters* for use in Singapore. Most of these characters were identical to the standard simplified characters used at that time in the People’s Republic of China, but 77 simplifications were different. Many of the different simplifications are the same as the earlier “first batch” simplified characters, and a few are the same as simplifications given in the later “second stage” simplification tables, but 23 simplifications are unique and unencoded.
In 1974 an expanded list of 2,248 simplified characters was issued, of which only 10 characters still differed from PRC simplified characters. Finally, in May 1976 a revised list of simplified characters was issued that omitted the 10 Singapore-only simplifications, and was now identical to the list of simplified characters used in the PRC.

* This is why this one is also referred to as 《502》.
Second Stage Simplified Characters (1977) (第二次汉字简化方案)
(From Page 21 of the Proposal)

Following on from the formal introduction of simplified Chinese characters in the 1950s and 1960s, an attempt to promote a second stage of further simplifications was made in the late 1970s. In May 1975 the Chinese Writing Reform Committee (Zhōngguó Wénzì Gǎigé Wěiyuánhuì 中国文字改革委员会) produced a first draft of Second Stage simplified characters for review by the State Council, and eventually on 20th December 1977 the final draft (entitled Dì'èrcì Hànzì Jiǎnhuà Fāng'àn (cǎo'àn) 《第二次汉字简化方案（草案）》) was published in the People's Daily (Rénmín Rìbào 人民日报), the Guangming Daily (Guāngmíng Rìbào 光明日报) and other newspapers (see Figs. 2-3 and Appendix C).



The draft comprised two tables, Table 1 with 172 individual simplifications and 21 generic simplifications, for immediate use; and Table 2 with a much larger number of simplifications for future use if the Table 1 simplifications proved successful. Table 1 only was added as an appendix to a new edition of the General Table of Simplified Characters (Jiǎnhuàzì Zǒngbiǎo 简化字总表) that was published in December 1977 (see Appendix B).
On 21st December 1977, the day after the draft was published, the People's Daily started to use the simplified characters listed in Table 1 only, and continued to do so until July 1978 (see Figs. 4-5).



Postage stamps issued between June and November 1978 also made use of the new simplified characters from Table 1 (see Figs. 6-10).



During 1978 the new simplified characters from Table 1 were widely used in newspapers, books, and publications of all kinds, but the experiment was judged to have been a failure, and in July 1978 a directive to stop using the new simplified characters was issued. Although the new simplifications were not used in official publications after the end of 1978, they were not officially withdrawn until 24th June 1986 (see Appendix H). Nevertheless, the new simplifications did not entirely die out, and were occasionally used in printed contexts during the 1980s. Even today simplified characters from Table 1 are frequently met with in informal contexts such as shop signage and personal correspondence.



There is a pressing need to encode the Table 1 simplifications, both in order to discuss the history of Chinese character simplification, and also in order to accurately represent those texts that are written using second stage simplifications. As an example, a web site about Chinese post cards (http://www.postcardxp.com/list.asp?unid=2144) has the following entry about a set of post cards published in 1986 that includes the second stage simplification for 罐 guàn “pot” in the titles of several of the post cards. The author of the web site is unable to represent this character, and is forced to describe it using its component parts.



Unlike the simplifications listed in Table 1 of the Second Stage Simplification Tables, which were widely used and are still widely recognized, the simplifications listed in Table 2 were not used in official publications such as the People's Daily (or in any printed books that I have been able to find) and most Chinese people are not familiar with them. However, there is still a need to encode these characters in order for historians of Chinese character simplification to represent the draft simplification tables in electronic format, and to discuss these abortive simplifications.
A number of the simplifications in Table 2 are based on cursive or vulgar character forms that are commonly found in printed and manuscript texts dating back to at least the Tang dynasty, such as Yuánkān Zájù Sānshízhòng 元刊雜劇三十種 and dūnhuáng biànwén jí 敦煌 變文集 (see Figs.12-15), and so encoding the Table 2 characters would also be of benefit to
Page 24 of 112JTC1/SC2/WG2 N3695 scholars working with old Chinese texts. Other vulgar simplifications found in texts such as these will be the subject of a future proposal.


The characters are listed in glyphwiki:
第二次汉字简化方案・修订草案 (draft)
第二次汉字简化方案・第一表 (Table 1)
第二次汉字简化方案・第二表 (Table 2)
Which comes in handy when you want to include some of them in a paper.