To be on a shoestring means to be on a very tight or limited financial budget, which is what they had suddenly gone from comfortable to.
Consider the staetement "They had suddenly gone from comfortable to living within a very tight financial budget and being behind on something as important as their mortgage.". Based on this statement, is "They had suddenly gone from comfortable to living on a shoestring and being behind on something as important as their mortgage." a true statement? Yes/no/unknown