Yes, it is perfectly safe. An outlet is just a place where electricity is available when you need it. It can do you no harm whatsoever by sleeping next to it any more than sleeping next to a electrical cord plugged into that outlet and then run up to a lamp or clock next to your bed. I assume you are worried about the magnetic field created. This field is so low that it is barely detectable at an outlet.
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outlets thats one!
Yes
To be safe
Older style wires and cables are not as safe as the current types used for house wiring. For example, older insulation becomes brittle with age and can break when the wire is moved. Newer wiring is a lot more flexible and can handle age much better than the old insulation. Newer wiring specifications require that all circuits include a connection to ground, older outlets do not have that requirement. Newer outlets are far safer, not just because of the ground wire but because of the plug polarity that has been introduced to the newer standard.
It may have tripped a spark gap or GFCI breaker.