It's wild what some tanks can endure! The tank you acquired sounds like a classic case of a heavily-stocked, "natural" system, where the ecosystem has found a bizarre and precarious balance.
Here's why it's likely surviving, despite the lack of traditional maintenance:
* Biodiversity and Self-Regulation: The tank is a miniature, self-contained world. The massive amounts of Kenya tree corals and bubble-tip anemones are acting as a significant biological filter, absorbing nitrates and other waste products. These corals are essentially pulling double duty, acting as both showpieces and a natural filtration system.
* The Power of Top-Offs: The owner's wife was inadvertently doing something crucial: maintaining salinity. By just topping off with fresh water, she prevented the salt level from getting dangerously high due to evaporation, which would have killed everything quickly.
* Established Colony: The clowns and pistol shrimp have been in that environment for a long time. They've acclimated to the specific water parameters, even if those parameters are far from ideal. The numerous snails are also likely doing a lot of the cleaning work, breaking down waste and consuming algae.
* Canister Filter: While a canister filter isn't ideal for a reef tank, it's still providing some level of mechanical and biological filtration. It's likely trapping some debris and providing a surface for beneficial bacteria to grow, which helps process some of the ammonia and nitrites.
The fact that the anemones are looking a bit pale suggests they might be stressed or bleached due to a lack of nutrients or poor water quality. They're still hanging on, but they're not in prime health.
Be careful as you start to turn the tank around. A large water change could shock the system and cause a crash. A better approach might be to do a series of smaller, more frequent water changes over a few weeks to gradually improve the water quality. Also, be prepared for a massive die-off of algae once the water quality improves and you get the skimmer running—all that decomposing algae could cause a big spike in ammonia and nitrates.
Sounds like you've got your work cut out for you, and a lot of happy hobbyists will be lining up for those frags!