Should I buy a house that has termites?

They say it will be quick and cheap to get rid of them.

In real estate trading, if a deal seems unbelievably good, then it probably isn't to be believed.

A house that has been attacked by termites has lost some value.  It the attack has been severe or ongoing, then the value of the house is way down.  Remember that buildings weakened by termites are more likely to fail during severe storms.

Termites hide.  The damage they do is nearly all concealed and can only be seen by ripping things apart.  We can guess the extent of the damage, but we have to mess things up to be certain. Vendors don't like that.  Some vendors will try hard to conceal things that might make the house look bad.

To determine likely repair costs, you would need what is called an invasive inspection by the termite inspector and a building professional. This gets tricky. If the vendor will agree (in writing) to let your inspectors conduct an invasive inspection without either them or you having to make good any surfaces they choose to open, then it may be worth considering the purchase. Normally you would make an offer subject to the inspection works providing a repair cost estimate below an agreed figure (which you don't tell the inspector!). That gives you room to get out if the place really isn't worth it. You would want a good lawyer to draw up the contracts.

Chances are that a few more things needing fixing will be found during the partial demolition before repairs begin.  You could also be up for works to prevent immediate reinfestation.  All this adds up.

Bottom line is that it would have to be an extremely desirable house and a very appealing sale price.  Is this particular house really worth the risk?