[danhon]

In your first case, I'm pretty sure I've seen contracts that require the repayment of e.g. relocation costs if the employee leaves within x time period.

[madcaptenor]

I was recruited with paid relocation at my current job, and I would have had to repay relocation costs if I left within a year.

[sagarm]

Often a signing bonus also needs to be repaid (pro-rated).