I am considering transfering my bitcoins from coinbase to electrum wallet. My question is, what happens if Electrum suddenly shuts down and their servers go offline? Will I be able to access my coins using another wallet or will they be lost?
That's why you need to save the backup of the private keys of the electrum wallet. Whatever happens to electrum as long as you have the private keys and no one knows it besides you then you're safe just save it offline.