Why does this 32eth min exist?
For rolling back transactions, a 50% attack actually convinces the remaining honest nodes. For invalid transactions, even if you have 90% of the network, the remaining 10% of honest nodes will not follow the wrong chain.
This means anyone could detect this happening. At which point faith in eth will plummet, and so will prizes.
https://launchpad.ethereum.org/en/faq
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How badly will I be penalized for being offline?
It depends. In addition to the impact of effective balance there are two important scenarios to be aware of:
Being offline while a supermajority (2/3) of validators is still online leads to relatively small penalties as there are still enough validators online for the chain to finalize. This is the expected scenario.
Being offline at the same time as more than 1/3 of the total number of validators leads to harsher penalties, since blocks do not finalize anymore. This scenario is very extreme and unlikely to happen.
Note that in the second (unlikely) scenario, you stand to progressively lose up to 50% (16 ETH) of your stake over 21 days. After 21 days you are ejected out of the validator pool. This ensures that blocks start finalizing again at some point.
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The penalty for missing one validation is small; the penalty for missing a block proposal is also not huge, but bigger than the penalty for missing a validation. Penalties would pile up over time if a validator is offline for an extended period.
Long story short: if you intend to run an ETH2 validator, you should be reasonably sure it will be able to run well-connected to the Internet for extended periods of time. Intermittent and brief periods of downtime would not have a substantial economic impact on your validator, but extended periods of downtime would be bad.