When the network lacks sufficient processing power to protect against attack
Take a look at CoinYe (West). There have been no trades since 2017 and the currency is considered defunct. Essentially Kanye West sued them for using his name and likeness, and the original developers dumped their coins.
Interest waned and the network lost 99% of its processing power, and the coins lost essentially all of their value.
Remember, cryptocurrencies count on the built in redundancy of thousands or millions of independent servers, each run by someone who holds that currency and wants it to be as secure as possible. If you don't have a critical mass of investors, then it's pretty easy to orchestrate a 51% attack such as the attack on Ethereum
To drive this point home even further, crypto51.app has listed prices per hour to perform 51% attacks on most cryptocurrencies.
A commenter mentioned "Loss of Quorum" - this is the technical way of saying there are not enough 3rd party observers to validate any future transactions.
All cryptocurrencies work by having 2 entities announce their transaction in public (the internet). If it were in English, it would sound something like I Jack, would like to give Jill coin #723.
The 3rd party observers all pull out their ledgers and look. Jack owns coin #723 so this is legit. Over the next little while they confer with each other and all agree Jack really did own coin #723 and gave it to Jill. They all add this transaction in their ledgers.
If only "a few" of the observers disagree, they are shouted down by the rest of the observers and agree to change their ledgers.
That last sentence is the key to understanding attacks
Now for the 51% attack - Jill has a majority of the 3rd party observers in her pocket. She decides to sell coin #723 to Bob, Ashley, and a whole bunch of other people. She can get away with this because her gang of 3rd party thugs is larger than the rest of the group put together, and they will convince everyone she only spent the coin once, when in fact she spent it multiple times.
Jill has a short window to "double spend." It won't be too long before all the duped people start talking and realize that Jill has the town in her pocket, and simply stop accepting coins as payment. All that's left are the criminal scum who agreed to rig the system to begin with.
This leads to a Loss of Quorum. Essentially when none of the 3rd party observers trust each other enough to agree on anything. Even if one or two new people join in, they don't have the critical mass of observations needed to ensure the integrity of the system, and the whole thing falls apart.
In this example Loss of Quorum is when there are not enough 3rd party observers to "shout down" the hold hold-outs with a unified narrative of what happened.
EDIT 2: Why this doesn't happen more often
Some commenters have pointed out that the market capitalization is worth a lot more than the cost of a 51% attack, so why aren't these occurring everyday?
Mainly because an attacker really only has one shot at this. They've got to first hoard as many coins as possible, then attack and convert those coins to cold, hard, cash. The market for digital currency, especially lesser know ones, is only so big, and finding buyers and doing the transaction takes time. All this time eats into the profit.
The market is open, so players will notice someone is suddenly unloading a lot of coins all at once, which will raise suspicion. Once an attack is suspected, people will simply stop buying coins until things are sorted.
Now the attacker, who either bought coins, or spent a lot of time mining them, is stuck with whatever he couldn't unload. The attack also drove down the value significantly, probably to $0.
The attacker has to guess just right. Too many coins and they'll be left holding a lot of worthless digital currency. Too little and the attacker doesn't get a large enough pay-day to cover cost and risk.
It also looks like some people are doing 51% attacks to draw attention to the issue https://bravenewcoin.com/insights/attacker-pledges-to-make-51-percent-attacks-a-spectator-sport