This sounds like a bent rim. If so, no amount of truing will make it a good wheel. It needs to be bent back to close to true, the trued as usual to the best that can be achieved.
Bike shops used to have 'dent pullers" (that also wore several other names) designed to pull out inward bends. They looked a little like a dishing tool only narrower and far stronger with a solid hook that laid flat against the inside of the rim. You loosen the spokes over the indent, place the tool against the outside of the tire (left inflated on the rim to protect it), tighten the screw to bring the hook against the rim then tighten further to pull the rim out to just past the surrounding area. Tool off, spokes tightened and if done right, rim is quite ride-able. (The metal will work harden and not "unbend" perfectly so the end result will not be perfect or beautiful.)
This fell out of favor with the new, much stronger aluminums that are nowhere near as malleable as those of the '70s. And with today's lawsuit crazy environment, those tools are now a big liability to shops. I think they are now all stored in a facility resembling Fort Knox. I want one. I'm now building wheels to ride using old tubular rims but things have happened to them both on-bike and accidents in storage, etc. So if any of you reading this has one that should be sent to that fort, you can send it to me and trust that the only rims it ever touches will be mine.
And funny story - re: wheels with side-to-side bends. Here, that tool is no help. But like the inward dents, only bending back to straight will make good good repair. At the shop I worked in, those wheels went to our master mechanic. He'd tell the customer it would take hours and to come back later. Customer out the door, he'd loosen the appropriate spokes, grab the wheel (again, tire on and inflated) and slam the sidewall on a concrete step. Tighten nipples and be done. 10 minutes. (Customer sent away simply so he never saw that!)
Until modern aluminum, these were standard practices.