In that case: not all the time everywhere, but yes, mixing envelope material down into the core and pulling heavy elements out (and then all the way out, through controlled CMEs) is an important part of prolonging hydrogen burning in a star.
Brown dwarves and rogue gas giants, mostly.
Slooooooooowly.
But fortunately, you have even more warning about when you need it than you have for the million-year atmospheric replenishment schedule, so you have plenty of time to plan for your top-up to light-sail-gravity-tractor itself across space and into your outer orbits just in time for the scheduled switching of a couple of your particle geysers from blow to suck.
Yes. Bring inflammable spirits, and bring them by the keg.
Not enough to make them any less dangerous.