I am not sure what happens if someone moves abroad but my experience tells me that debt collectors rarely seem to give up here in the UK.
15 years ago, the other half to my semi was owned by a chap who moved out to the Middle East to work on various oil contracts. He was an old friend and he left me a key and gave me permission to show prospective tenants around and even vet them for him, on the basis that if I thought they were going to be good neighbours, then they would also be good tenants for him.
It worked out very well for years until one couple did a runner owing huge sums of various store charge cards. It was estimated that they went into every major High Street Debt shop and started cards with them all. They had Boots Cards, Debenhams, John Lewis, etc, etc. They were always having expensive household items delivered.
Collectors continued to call for nearly 3 years, even when new tenants were in place. This was 5 years ago, and the present person who now lives there
( he bought it from my friend) still receives letters addressed to the previous tenants !