It’s possible to leave the oil (or propane, natural gas, wood) boiler in place and tie your new pellet boiler in with it. You will most likely need a separate flue, particularly if there’s a chance that both boiler may run at the same time. That is the case if, for example, a smaller pellet boiler is installed with the intention of having the oil boiler supplement during the few hours of the year when the head load is greater than the pellet boiler output.
It’s more common to have an oil back-up with a manual-clean pellet boiler. Automatic-clean boilers are designed to be left alone for long stretches, so there’s no need for back up with those (unless as stated, a second boiler is desired for supplemental purposes).