Can't start Linux after deleting core dumps

My root partition had no space to the point that couldn't login. So invoked Ctrl+Alt+F2 and ran to free disk space:

find / -xdev -name core -ls -o  -path "/lib*" -delete

Now can't even initialize OS after GRUB, it days:

run-init: can't execute '/sbin/init' No such file or directory
run-init: can't execute '/etc/init' No such file or directory
run-init: can't execute '/bin/init' No such file or directory

How can solve that?