There are 2 ... assign ... which is the newest ... and assignment (2.2) ... the older no longer should be/can be used.
Which did you delete?
Fix ... download the version of moodle you have (seen in Notifications). On local computer unzip/un-compress. Find the 'assign' or 'assignment' folder in the unzipped/un-compressed local copy. Upload via whatever tool you have to upload to the mod directory of server which ever one you deleted.
Check ownerships/permissions on newly upload folder to match that of other folders in mod.
As admin, visit Notifications ... that hopefully will trigger re-install of that which you deleted.
Comments: in the future, never delete anything core code ... if not using, hide it or dis-able it. Also, not sure if any student work your server had in 'assignments' will be present still.
'SoS', Ken