So I've been working with wormholes and portals extensively with my writing and can probably give you some pointers. I'll be describing them as portals from here on. It's also important to note these portals reduce the distance from one point to another to 0, meaning I take one step and feel no different than normally walking, yet I just crossed light years of space.
I have two kinds of portals that work. One only requires creation and stability at one end, so you could make a connection from, say one solar system to another. This has to be done outside of the system, so generally around the region of the kuiper belt or farther (please note this depends on the system in question, you would be able to do so closer or farther if the solar environment allows for it). This system needs a massive power source in order to maintain the portal, but it is possible. It's also quite safe, just don't touch the edges of the portal.
The other kind uses two connection couplings. Structures that pull the portal open while pouring power through to stabilize it. These tend to give off lots of excess energy, something detectable by today's standards.
If the portal is naturally occurring, then there's a reason and it's probably very big. A man made portal that loses power simply collapses and disperses with everything returning to normal since there's no energy to do anything else. A natural portal would take such immense energy that even being nearby would probably be fatal. So if it's not a natural portal, it wouldn't end up being a black hole after it closes.
If instead you are talking about a place were there is a convergence in the dimensions that allows for accidental transfer, then this might work. Basically through issues in the surrounding dimensions the local space is weak, and it would look very strange. Odd lights and hues of different colors dancing around, sense of direction would be lost, gravity would behave strangely and so forth.
Also please note: Creation of portals across vast distances takes lots and lots of energy, I'm talking the power of the stars here. The longer the distance, the less viable it is. A very long distance portal, say between galaxies, is unlikely then. After all, if you can create such a thing, why bother with Earth? I'd find your story more likely in this sutation if the connection point was at least in the solar interstellar neighborhood (which is a real thing).
For your story, any of the following work:
- The portal is opened by a long forgotten starship AI that's crashed on a planet, trying to find help
- The portal is like a trap, to lure people from one planet to another for reasons you can work out
- Somehow the wrong coordinates keep getting input wrong in whoever's portal creation system, breaching intergalactic law about contact with primitive people
- To close the portal, you have to get some high energy output device so it can't maintain it's shape. However, said portal is not only underground but well defended. Maybe earth is being slowly invaded?