The crossword solution for the term 'BACKS OUT, WITH 'OFF'' is 'BEGS'. This term is used to describe a situation in which someone withdraws from a commitment or agreement, usually due to fear or uncertainty. It is often used in the context of someone who has agreed to do something but then changes their mind and decides not to do it. The phrase 'backs out, with 'OFF'' implies that the person is backing away from the commitment and leaving it behind.