Compact objects (COs) can exist and evolve in an active galactic nuclei (AGN) disk, triggering a series of attractive CO-related multimessenger events around a supermassive black hole. To better understand the nature of an embedded CO and its surroundings and to investigate CO-related events more accurately, we study the specific accretion process of a CO in an AGN disk and explore the role of outflow feedback. We show that the asymptotically isotropic outflow generated from the CO hyper-Eddington accretion would truncate the circum-CO disk and push out its surrounding gas, resulting in recurrent formation and refilling of an outflow cavity to intermittently stop the accretion. Applying this universal cyclic process to black holes (BHs) and neutron stars (NSs),we find that, even if it is above the Eddington rate, the mass rate accreted onto a BH is dramatically reduced compared with the initial gas captured rate and thus consumes little mass of the AGN disk; outflow feedback on an NS is generally similar, but possesses complexities on the existence of a stellar magnetic field and hard surface. We demonstrate that although outflow feedback itself may be unobservable, it remarkably alters the CO evolution via reducing its mass growth rate, and the AGN disk can survive from the otherwise drastic CO accretion overlooking outflow.