Is it possible to make a permanent partial denture for a person who still has damaged teeth left?

Possible: Yes, it's possible. However, if your teeth are very damaged your dentist will probably recommend that you have them treated or removed before deciding whether a partial or full denture is the best plan for you.

Not advisable: If you are referring to an implant supported prosthesis (fixed partial denture), or tooth supported "bridge", then you are best to wait until the areas are all healthy and at least temporarily restored. You want the foundation to be stable and healthy for either treatment, and the remaining treatment to be planned and predictable.

Yes, but....: It is best to have the damaged teeth repaired as best as possible to provide for the best result. Especially those teeth which support the partial denture must be restored well.

What's best?: Anything is possible. Doing the right or best thing is a different story.Getting advice over the internet in these cases is the least sensible way to approach the problem.You need to have a dentist actually examine you, take a complete set of x-rays, & then sit down with you to discuss all treatment options, prognosis of each, pros & cons, etc. Then you can make an intelligent & informed decision.

Yes : This is possible. It depends on the stability of the remaining teeth, medical issues, the bone structure around the teeth and the location of the teeth in the mouth. See a dentist for a consultation.