Unfortunately, I don't think that is the case. Pseudomonas aeruginosa for example has a high incidence of carrying a particular bacteriophage that helps it resist new phage therapies used against it. But it continues to carry that phage even after developing tobramycin resistance.

Starving out bacteria is not going to be a good option. Most bacteria are much better at creating the molecules and proteins they need using very little resources. Some have extra metabolic pathways to make things in ways that our body doesn't. That's why in the lab we can grow some bacteria on very minimal media that has only a single molecule for a carbon source (like glucose) and a single molecule for a nitrogen source (like ammonium sulfate) and they can make everything they need to continue growing with just those two things.