In MIT's ARC design, the reactor is designed so you can easily open it up and replace the inner vessel. The vessel is 3D-printed and replaced once a year. Surrounding the inner vessel is a molten salt mixture which breeds more fuel from lithium but is otherwise unaffected by neutron radiation.
This is a regular tokamak design, with a high chance of success since we understand tokamaks very well at this point. Various startups have more speculative designs that deal with the issue in other ways.
A single ARC reactor will use 40% of the world's annual production of beryllium.
The power density of an ARC reactor will be around 0.5 MW/m^3. In comparison, the power density of a PWR reactor vessel is 20 MW/m^3.
Replacing the entire inner vessel once a year would be an operational nightmare. For one thing, it ensures the building the reactor is in will have to be very large, with very large secondary bays where the intensely radioactive material of a spent reactor vessel can be moved and disassembled (generating radioactive fragments and dust).
Boron, however, is more easily concentrated (in evaporites). Beryllium is found in pegmatites, which are less common. The estimated resource (not reserve) of Be is 100,000 tons (USGS). This would be enough for ARC reactors supplying just 1% of current world primary energy demand. The estimated world resource of boron is in excess of 1 billion tons.
This is a regular tokamak design, with a high chance of success since we understand tokamaks very well at this point. Various startups have more speculative designs that deal with the issue in other ways.