Beg, coming to a bad end in prison! (5)
I believe the answer is:
cadge
'beg' is the definition.
(I know that cadge is a more specific form of beg)
'a bad end in prison' is the wordplay.
'end' indicates one should take the final letters.
'in' is an insertion indicator.
'prison' becomes 'cage' (cage is a kind of prison).
The last letter of 'bad' is 'd'.
'd' placed inside 'cage' is 'CADGE'.
'coming to' is the link.
(Other definitions for cadge that I've seen before include "get free" , "Scrouge, ask for" , "Bum" , "Caged (anag.)" , "beg" .)