Old light wires Question

I just moved into a home that is about 50 years old and noticed one of the kitchen lights wasn’t working. The light would work only some of the time. I took out the light bulb and unscrewed the panel and noticed some black crap(turned out to be old old electricity tape) and some wires that were dark brown, almost rusty looking. Well it turns out the wires disconnected at the base (where the light bulb screws in). Before I checked one was only disconnected, but as I opened the panel the other wire snapped and the ceramic unit crashed into the sink. So now I had 2 rusty colored wires dangling. I taped them off with new electricty tape and put back on the panel.

My question is, is this okay until they get replaced. I am concerned these old wires pose a fire hazard. The old tape is still on (where the old wires connect to the house wires) and I want to make sure nothing bad will happen as long as they are not moved anymore. I didn’t smell any smoke or notice any sparks or ozone or anything so I think it is okay but I want to make sure.
it sounds fine. as long as you clip the ends off of them and tape them well it isnt a big deal
This is why I hate electric tape. I only ever use it on outlets (tape around the exterior to make sure they don’t slip and short). Wire nuts >>>>>>>>> electric tape

Yeah nothing has happened yet so it seems okay. I am getting a general contractor (friend of my dad) to take a look at it. It seems like a minor repair though.
Had a contractor look at it today, turns out the wires were burned all the way down to the light and were crossed.

He put in a double grounded plug instead and now I have a pull down string where the new light is.