By design, the modified spike proteins created in a vaccinated person's cells from mRNA and adenovirus-vector shots remain anchored within the cells but protrude through their cell membranes so that they can be readily "seen" by the person's immune system.
What do you think happens to the cells in question? That they live out the remainder of their lifespans unmolested? They are destroyed.
Much of the promise of safety at the outset rested on the belief that the contents of the vaccine doses would remain localized at the injection site (muscle in the arm in most places afaik, but the jabs are also given to some people in some places in their thighs). For the mRNA covid vaccines, at least, we know that the doses do not stay in the arm but travel throughout the body and even, in some cases, into breast milk. When the data about dissemination of the mRNA shots contents began to raise alarm bells, there was a period where some medical professionals blamed it on a failure to aspirate the needle before injecting and hoped that those who'd been injured had simply been unlucky and the person administering their dose had hit a blood vessel.
We've gone from, at the beginning, recognizing that wide distribution of the mod-spike-producing covid vaccine dose contents throughout the body was dangerous but believing that it wouldn't be an issue (because we're administering into muscle tissue in the arm) to knowing that the dose doesn't stay in the arm but completely forgetting why we hoped that it would stay there in the first place.