AUTUMN COURT

for starters:

as learned in sotr, there's no reason to believe anything about an arena unless we're learning something from the victor of that arena. anything else can be propaganda. for example: i thought the volcano in haymitch's arena was one that erupted entirely on its own. in sotr, we learned it was gamemaker made. what's not to say that the dam in annie's arena isn't gamemaker made, too? and they could've had sea mutts in it? while the likely hood of that is low, it's not nonexistent: with so little about it known in canon, anything can be on the table.

now: if an earthquake broke the dam in arena's arena, then that would most likely place her arena on the west coast of the united states, likely within the pnw region. an earthquake strong enough to break a dam would have to be 7.0 or above: and that can vary as well, because the lower magnitude the earthquake is, the closer it would have to be to the dam.

an earthquake strong enough to break a dam would also be one strong enough to be near cataclysmic to that region and to those surrounding it: and once again, with her arena being in an area prone to earthquakes and with natural dams rather than gamemaker made ones, that would yield horrific results to district four, which would be nearby and on the same coast. aftershocks, tsunamis, etc .. that would absolutely bring forth death to four and particularly to those working within the water or living near it. while i'm sure the capitol is skilled at withholding information, this is something that i'm sure would have been either mentioned by a victor, or well known to panem.

regarding dam infrastructure: most dams within the pnw built prior to 1990 will not be able to withstand an earthquake above a 9.0, which is why i lean towards an earthquake breaking the dam in her arena being that strong.

in terms of finnick blackmailing a gamemaker to break a dam that isn't gamemaker made: i'm egyptian, and my family lives in a city on the coast. the ocean is perhaps our greatest love: and we know to fear it, because it's very unpredictable. only six inches of water can knock you down. in breaking a dam, being a strong swimmer isn't enough to guarantee you survival: there's the matter of i'm assuming debris, anything that's caught within the water (animals, trees, logs, also debris), and then currents: you cannot guarantee someone's survival with currents. it's entirely unpredictable: anyone wary of water and who knows to respect it would not subject someone to that, because that is extremely dangerous and unreliable.

i think the most likely option to me would be beetee's meddling: i saw on one post that his son would have been nineteen by annie's games. that could point as to why we haven't heard anything about his son. but also, one can argue that he would have mentioned in the books if his second son was also killed by the capitol.