Speaking of this sort of thing, my doctorate class was rather
interesting. We had one military intelligence instructor from
Israel, a military psychologist from the UAE, plus one more from
Indonesia. The Indonesian fellow was attached to Kopassus, and we
had a jolly good time trading tall stories over drinks about our
first airborne jumps. The Israeli fellow was stationed as a
plainclothes officer in Lebanon until he got made - they shipped
him back out to Israel ASAP and he finished his service as an
instructor. In any case, all of these guys were pretty cagey about
security, and watching all of them in the same classroom was a
barrel of laughs. 
Anyway, back to the topic. Now, forgive me for with mixing business
strategy with political/military strategy, if I discovered a
liability, the first thing I'd be thinking about would be how to
turn that liability into an asset.
Short of busting into the room while the spy is transmitting the
message, it is possible to keep the discovery of the spy a secret
from the spy him/herself. Now would an unaware spy not be more
useful feeding our misinformation back to their country than being
sent back in pieces as a message? Personally, I'd be happier having
my enemy foot the bill while I run rings around him feeding him the
wrong data. 
Of course, I would only do this if the spy was strictly in the
business of collecting information. If the fellow was planning to
carry out an attack, I'd just liquidate him very quietly if
possible. There's no need to advertise that sort of thing -
investor confidence can be shaken by the knowledge that you're
definitely the target of a terrorist attack. Besides, there's
nothing that gives the bad guys more heebie-jeebies than the
unknown.