[lelio]

PO Box 34567 is currently good in Houston, TX but at zip code 77234-4567.

Zip codes change, especially when a city grows a lot as did Houston.

As for PO Boxes -- are the numbers recycled? Are they only good for one city?

[TXBSAFH]

I would hate to be the poor sod who has this box now.

[ASA Vet]

Yes, zips change, but usually it's due to expansion
the old zip still will exist.
Generally if it's due to expansion a new zip will be assigned to cover
some of the area under the old zip.
USPS doesn't move the zip to somewhere else.

77034 still exists.

PO Boxes used to be numbered one up in each Post Office, so PO Box 1 might
exist in Detroit, New York, and thousands of other Post Offices.
Now in large offices they are generally assigned by
the local Post Master to the various stations, branches, and annexes in numerical blocks.
Many larger offices will assign a unique zip code to a PO Box section.
Example: 49501 is the box section in Grand Rapids main office,
while 49514 in the box section at the Grand Rapids NW Station.

[ASA Vet]

Further information.

Zip codes 77034 and 77234 are both located at the same USPS Station.
77234 is the unique zip assigned to their PO Boxes.
77034 is one of their street delivery zips.

It's probable that 77234 is an expansion zip to handle the box section
and that 77034 would have been correct several years ago for their box section.

I certainly wouldn't wish to be the renter of that PO Box today.
I'll bet they've had a visit or two from folks with big gold badges.