During my last game, I had some enemy forces chasing around my undefended flagship. We both had the same movement points, so I had to be very careful. I managed to stay out of their way long enough to reach an influence starbase I had in their territory.

The starbase had the first battle upgrade and a devastator beam for defence. I parked the flagship under it so that it wouldn't be destroyed. And then I saw something crazy...

The pursuing ships tried to attack and died on the starbase. I sat my ship there for a while, and over time, a string of small vessels from nearby planets threw themselves onto my defences. Over a couple of dozen turns, they did manage to destroy the starbase, but not before losing a ton of ships.

I haven't tested this with a more heavily defended starbase to see if I get the same effect or not. It could be that they decided the damage caused was worth losing the ship, but I want to be sure. It could be that the ships try to attack my 0-ATK medium class ship (a juicy target), and just don't 'see' the enormous base standing next to it.