Examples of finishing solvents include mineral spirits (paint thinner), naphtha, denatured alcohol, lacquer thinner and acetone. None of these products have a shelf life, unless they evaporate because you’ve left the can open, and none can spontaneously combust like linseed oil can.
Of course, all of these solvents, with the exception of those that contain water, will feed a fire that is already going. So you should still be careful where you toss rags that are wet with solvent. But no amount of these rags, piled into a trashcan, will start a fire by themselves.