When is f not pronounced? I've seen that in Beijing Mandarin f can be pronounced as something of a final consonant when in an unstressed syllable, e.g. 豆腐 dòu fǔ = dòuff.

However, in other cases it disappears in unstressed syllables. One example is that in Beijing dialect 王府井 is pronounced as " 王五井", Wáng wǔjǐng becomes wángfǔ jǐng ( http://www.360doc.com/content/18/0123/07/1260016_724326694.shtml ).

Is this because of some kind of tone rules? Both of the "fu"s are third tones in these examples. Are there cases where both the f and the final of that syllable are pronounced in colloquial speech?
This is a typical example of slurred speech in colloquial Chinese. Just like we say &quot;I'm&quot; instead of &quot;I am&quot;, &quot;kill'em&quot; instead of &quot;kill them&quot;; &quot;kinda&quot; instead of &quot;kind of&quot;, &quot;gonna&quot; instead of &quot;going to&quot; in English.
While we usually represent these verbal shorthand by way of contractions (as demonstrated above in the first 2 examples) in English (and also in French), there is no conventional way to do so in Chinese, because morphemes are mostly monosyllabic - which means, you risk losing meaning by blurring out the sound when spoken and/or obliterating the character when written (Abbreviations are another matter) - which makes representing slurred speech on paper difficult.
Curiously, there are certain characters that are meant to be contractions and pronounced that way. For example, 甭 béng = 不用 bú yòng in Peking speak；and 諸 zhū = 之乎 zhī hū in Classical Chinese. These would be the true formal contractions that can be written down as-is. But such cases are scarce.
This makes it especially hard for new learners to grasp the nuances in the slurred verbal expressions because they are not familiar with the standard, formal way of pronouncing that term or phrase, and there is no proper way of representing that kind of speech in writing.
I would see the example cited by the OP above as part of a wide range of verbal corruptions that happen frequently in day-to-day speech. Other examples would include:

&quot;大家&quot; dà jiā pronounced as dà-ā (very common in Taiwan); or
麵包 miàn bāo pronounced as miàM-bāo, in which the interdental n consonant is pushed forward (i.e. corrupted) by the bilabial b that
immediately follows to give a m.

These should be differentiated from the formal rules that dictate pronunciation and tone in speech.