[en] Central compact objects (CCOs) are a handful of young neutron stars found at the center of supernova remnants (SNRs). They show high thermal X-ray luminosities but no radio emission. Spin-down rate measurements of three CCOs with X-ray pulsations indicate surface dipole fields much weaker than those of typical young pulsars. To investigate if CCOs and known radio pulsars are objects at different evolutionary stages, we carried out a census of all weak-field ($<<!--\; <\; -->{10}^{11}$ G) isolated radio pulsars in the Galactic plane to search for CCO-like X-ray emission. None of the 12 candidates are detected at X-ray energies, with luminosity limits of ${10}^{32}-<!--\; ???\; -->{10}^{34}$ erg s⁻¹. We consider a scenario in which the weak surface fields of CCOs are due to a rapid accretion of supernova materials and show that as the buried field diffuses back to the surface, a CCO descendant is expected to leave the P–$\stackrel{\dot{}<!--\; ??\; -->}{P}$ parameter space of our candidates at a young age of a few ×10 kyr. Hence, the candidates are likely to just be old ordinary pulsars in this case. We suggest that further searches for orphaned CCOs, which are aged CCOs with parent SNRs that have dissipated, should include pulsars with stronger magnetic fields.