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I have not trusted them with my password so I can't say. I'm not sure you can access the wallet either.
If wallet security was an issue, I think you can log in using your posting password.

Do you know of a way to access your steem wallet if the steem website was to ever go down for good? This has been on my mind alot lately.

Not at the moment, though if the other sites have access to the wallet, you should be able to use that as long you have the wallet password stored somewhere that isn't steemit.com.

I think a dev, or at least someone posting in the dev tag, is working on a client that will run on your PC rather than running it on the website as happens now.

https://steemit.com/steemdev/@armandocat/steem-steemit-full-decentralization-problem

So some people are working on the issue, and with a better solution than merely keeping one website up.

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