What model do you own, and how old is it? That matters more than the company's troubles right now.
The supply chain for Raleigh parts doesn't disappear the moment a parent company hits financial problems. Most of their components - hubs, derailleurs, brakes, chains - are standard stuff made by Shimano, SRAM, or other third-party manufacturers. You can source those from any bike shop or online retailer without needing Raleigh's blessing. Frames and proprietary bits are trickier, but unless you've got a rare model from decades ago, you're unlikely to need those soon anyway.
Where it gets sticky is with older or unusual frame sizes and specific groupsets they spec'd. If your Raleigh uses common sizing (54cm, 56cm, etc.) and standard components, you're fine indefinitely. Hunt down parts through general bike shops first, then eBay or specialist retailers if needed. The real gamble isn't whether you can fix what you have - it's whether buying a new Raleigh right now is smart, since warranty support and recalls could evaporate quickly. If you've got one already, keep it and maintain it normally. If you're thinking of buying, there are plenty of other solid brands with stable ownership.