"that deserves," 1570s, present-participle adjective from deserve (v.). Related: Deservingly (1550s). Phrase deserving poor, those in need and unable to work through no fault of their own (the old, the sick, the lame, etc.) is by 1801.
the deserving poor
a deserving cause
deserter
desertification
desertion
deserve
deserved
deserving
desex
desexualize
desi
desiccant
desiccate