It can be a right bollocks with some races, it can be really hard to get a bearing extractor to grip on what’s left but I’d definitely start there just because it’s nondestructive. IME it doesn’t leave many easy options if that doesn’t work…
1) weld a tab onto it. Obviously most people can’t weld so that’s an issue but it’s the best way if you can or you know someone who can. The heat shock helps too.
2) cut the race. Impossible without damaging the hub a little, hard to do without damaging the hub quite a lot. Well, not hard exactly but it’s so easy to give in to frustration or carelessness. Can be impractical depending on the design.
3) Drill into it from the opposite side so you can get a solid hit onto the race. Again, can’t be done without damaging the hub and can be just really bloody difficult with the shape of things.
4) try and get a chisel between the race and the hub from the side. Will always mar the hub a bit and can be very awkward.
Might be others I’m overlooking so don’t take that as a complete list. Heat and cold can help too but tbh it’s really pretty difficult to get a useful amount of cold into it. (heat is sort of the wrong way round as it’ll expand the race in the hole, but that can still flex the parts enough to loosen things a little, break corrosion bonds etc)