Well, for one, we have no idea if Depletion Garden would break the link because prana is being directly transferred from the mage. It's not from the surrounding environment, and safely stored within their Circuits. And while few Servants can survive after their Master is killed, really all they need to do is leech on souls/mana until they run out of necessary prana to sustain their existence, hence why Caster is still around despite not having Independent Action.
She's not an ancestor, but a regular Dead Apostle. Innately hard to kill doesn't mean impossible either, the Church and White Princess puts them down repeatedly. The only real exceptions are Nero, who had to get the death of concept treatment, and Roa who had to get either that or Ciel's weapon. The rest are either too powerful to fight anyway or stay hidden well.