Spare parts and maintenance are likely going to be a problem first for ICE owners, rather than fuel availability. Who would be crazy enough now to invest in (and maintain) a factory for producing ICE-specific parts? Parts and skills for ICE will become scarcer and more expensive, making a new EV look economical to ICE owners in very short time. It has already been a few years now where it has been uneconomical not just to build a new fossil fuel power plant, but also to continue operating them due to maintenance costs. I'd suggest the same thing with ICE vehicles--it becomes easier/cheaper to run an EV rather than an old ICE quicker than people may usually assume.
The biggest cost of producing parts is making the tooling to mass produce them. Manufactures will retool to produce other stuff once they have enough of a given part, but if there's a shortage (or they think there will be one soon) they'll bring the old tooling out of storage and set up the line again. It's common for auto companies to supply new parts for decades after a car is made.
Heck, Mazda makes new parts for the original Miata.[1] While the first generation Miata is a recognizable car, it's not very popular. A total of 433,000 were produced. Maybe half are still on the road today. That may sound like a lot, but twice as many Ford F-150s are sold every year. If it's profitable to keep making parts for 200,000 vehicles, it's going to be a long time before most ICE cars run into shortages.
The investment in parts is already made. All they need to do is not scrap the tooling. Until the car the part went to is 15 years old that isn't worth doing as you will make more from selling parts than from the cost of storing the tooling. Common parts like filters will be around for much longer. Parts that rarely break will have the tools destroyed sooner, but with millions of ICE cars on the road there will be a lot of needs for parts even if the need is less than today.
