the (former) employee keeps them (i imagine for a myriad of reasons like hygiene and various overheads it would take to track such)
things like tools (wrenches, drills, bits, etc) are separately supplied by the company per department/work area (sort of like hot desking in the office world) and stay with the company at all times
Guess it depends on field and where ya work. Places I've worked at will provide tools that you then keep. Only things I haven't kept are "Borrowed" tools which are your couple grand diagnostic tools, or other similar items.
All drills, anything I've bought through tool allowances, and the such, I've kept.
things like tools (wrenches, drills, bits, etc) are separately supplied by the company per department/work area (sort of like hot desking in the office world) and stay with the company at all times