Shut-in is good but it might be meant to apply to someone who is kept indoors for valid reasons such as illness. There is the term "cocooning" for living at home as much as possible, having groceries delivered, etc.

Posslq, as tsuwm mentioned, works, but I haven't heard it used much lately. For the act itself we have the terms "living together", "playing house" and "shacking up", in ascending order of colloquiality.

We speak of "throwing good money after bad" to indicate an investment that ends up costing us more than it's worth. Your used car example is a good example of this.