Criminal's proposal to finish inside (8)
I believe the answer is:
offender
'criminal's' is the definition.
(I've seen this before)
'proposal to finish inside' is the wordplay.
'proposal' becomes 'offer' (I've seen this before).
'to finish' becomes 'end' ('end' can be a synonym of 'finish').
'inside' indicates putting letters inside.
'offer' enclosing 'end' is 'OFFENDER'.
(Other definitions for offender that I've seen before include "Wrongdoer" , "guilty party" , "miscreant" , "Criminal" , "causing resentment?" .)