[ehPReth]

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

[Zooti]

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.