What hymns about death were common in the early 1400s? I am writing a novel and would like to know what hymn a family might have sung as their loved one died - in 1405 in England.
Fourteenth to fifteenth centuries England was Catholic. The most common hymn sung by the faithful could possibly be the Latin hymn: "In paradisum". This hymn is still quite popular and I have sung it on many occasions as the body of a defunct has been lowered into the earth at a cemetery. Traditional religious still sing this at the graveside of their brethren. 

Here it is played on YouTube: In Paradiusm - Traditional Catholic Requeim Mass

You may also want to check out the Requiem Mass for more pieces to be sung like Dies Irae for example.

Another possibility could be the Sub tuum praesidium which has always been a popular devotional hymn since Christian antiquity. It is still a Catholic tradition to recite the De Profundis (Psalm 130) in Latin for those accustomed to the Latin to be recited when visiting the graveside of those we love.


  Since the earliest times, Christians have sung "psalms and hymns and spiritual songs", both in private devotions and in corporate worship (Matthew 26:30; Mark 14:26; Acts 16:25; 1 Cor 14:26; Ephesians 5:19; Colossians 3:16; James 5:13; cf. Revelation 5:8–10; Revelation 14:1–5). 
  
  Non-scriptural hymns (i.e. not psalms or canticles) from the Early Church still sung today include 'Phos Hilaron', 'Sub tuum praesidium', and 'Te Deum'. - Hymn (Wikipedia)