Normally, department staff and/or the head of the department has a way to contact people on sabbatical. In a few situations, such as someone doing field work off the grid it might not be possible, but it usually is. Ask the department, preferably in person, to relay a request to the professor and for someone to reply to you soon whether it is possible for a recommendation to be sent.
The department will also know if the person is unreachable, in which case, look elsewhere for a letter.
Even HR has a forwarding address most likely, but may not be able to pass it on directly, though might through the department.
And the above is also likely to be true even when a faculty member leaves permanently.