They can also buy cases that have anti-tampering controls that force a poweroff if the case is opened but that is getting into more costly edge cases. The hardware exists but is not datacenter operations friendly. It is also possible to force a wipe of ram on a clean shutdown but one must assume this won't be. As one example the feds took Mega's servers from Equinix after yanking out the cables and out the door they went.
[Edit] I should add for completeness sake there are kernel boot options to clear memory space before allocation and after de-allocation with a performance hit. Both are enabled by default on modern kernels now.
init_on_alloc=1 init_on_free=1If you are really serious about security, you need to have a watchdog on network link downtimes because, no matter what, you can't disrupt a fiber optic network link without the server noticing.
Moreover, there is also the option to have distinct randomly-generated keys for each virtual machine, to make useless the speculative attacks that succeed to peek at the memory of another VM.
AMD has offered these options for years and the future Intel CPUs will also have them.