It depends on how deep the details are and how much the existing paint is clogging them. If it isn't too much of an issue, then a simple spraypaint reprime on top is acceptable.
If you are looking to strip a mini, it depends on the material of the figure and the paint type. I regularly use Super Clean to strip eBay second hand tabletop figures. It eats any paint I've thrown at it, without damaging molded plastic figures. However if it is a resin figure, the stuff will melt it.
Good tools once you've soaked a figure in your juice of choice are toothpicks and stiff bristle plastic brushes. Sometimes a resoak is needed. Once I've scrubbed a lot of the surface and picked out the details it is usually good. If original paint exists in a super obscure crevice, it shouldn't matter once new primer goes on.