If it happens to be sticky, like spilled food, or a greasy stain like spilled smoke fluid or too much oil, you can try dusting the object with cornstarch and leaving it awhile. I had a timetable with some kind of goo on it (looked and smelled like pancake syrup) and the cornstarch lifted it off. Since then, we’ve tried it on old delicate litho and it seems to work. You’ll know if the cornstarch starts to look grayish and clumpy. Just dust it off with a very soft brush and repeat as needed.
We’ve had decent luck on harder paint with tiny amounts of baking soda on a barely damp Q-tip, but even that might be too abrasive for a very old, soft stain.