Suppose the total energy release of a typical supernova is on the order of 1044 J, for a baseline. The question then becomes, if 100% of that energy goes into hurtling a physical object, how massive would the object be if the ejection speed was 0.1c?
At 100% efficiency (which is entirely unrealistic), the mass of the ejecta reaching 0.1c would be ~2 x 1029 kg or ~0.11 solar masses (or ~116 Jovian masses). This is also unrealistically small for a remnant core of a supernova.
Let's suppose we had a hypernova at 1046 J, just for comparison. Again, even with the unrealistic assumption of 100% efficiency the mass of the ejecta reaching 0.1c would be ~2 x 1031 kg or ~11 solar masses. This is more reasonable in that most cores of supernova are larger than one solar mass but the issue is with the assumption of 100% efficiency. Most of the energy in a supernova goes into the neutrinos and only ~1% goes into the blast waves that would accelerate the ejecta. So at 1% efficiency we are back at the original estimate for a supernova.
Suppose we invert this and impose a net energy imparted to one solar mass and find the maximum speed of the ejecta. For 100% efficiency and 1046 J, the speed of the ejecta could reach ~0.32c. If we are more realistic and assume 1% efficiency, then the net speed would be ~0.033c or ~10,000 km/s, which is still extremely fast for a one solar mass object. For a regular supernova at 1% efficiency, the ejecta speed is even smaller at ~1000 km/s, which is much closer to observed ejecta speeds as noted in other answers and comments.