Your funds are safe and you can always access them through a different Ethereum wallet interface.
Your funds and information are not ‘in’ MyEtherWallet (MEW). MEW is non-custodial, which means we don't hold or manage your assets. Your wallet exists on the blockchain itself, and MEW offers a way for anyone to interact with the blockchain easily. If MEW went down, you would simply have to find another Ethereum blockchain interface that would allow you to access your wallet.
The information used to unlock your MEW wallet – whether that is your private key, keystore file, or recovery phrase – is the same information that can be used to unlock your wallet on another platform. We always suggest doing the research before entering your information into an unfamiliar site.
You can also download and run MyEtherWallet locally. For assistance with that, read about using MEW offline.