I wouldn’t even recommend using ‘lite’ wallets like Multibit or Electrum, they use a blockchain on their own servers. If the servers for Multibit or Electrum were DDoSd, or crashed for any other reason, you wouldn’t be able to use your Cryptocurrency.
This is a bit misleading.
With electrum, even when you are offline you can see all your addresses and private keys.
If electrum servers all went offline, it's true you wouldn't be able to use your coins but
you could then transfer them to another wallet without too much hassle.