My next door neighbour has a broken basin plug hole.
There doesn’t appear to be a hexagonal nut securing the plug hole into the basin.
When the plug hole is rotated from the top, all the steelwork show in the first photo rotates.
I could remove what appears to be white rubber ring/silicone. But I’d like to know what’s under it first, as it’s not my sink.
Is there a screw in the middle of the plug hole as seen from inside the sink? Or a nut which is probably circular with two slots?
It looks like mine, which I suspect is effectively glued (siliconed) in place, and not designed to be removed. Hopefully someone knows different, or has a way to remove the insert assembly.
dremmel with cut off wheel and some patience 
There isn’t a screwthread in the middle of the hole.
There are slots which I have used to rotate. But everything rotate.
I’ve just tried to remove some silicone with a Stanley knife. It’s tough stuff, it’s not going to be easy.
I would try that if it was my basin.
It’s my neighbours, so I might not be so cavalier.
Not the way I would choose to begin my retirement!
I would suggest that you neighbour calls a plumber.
Hmm I had a leaky plug hole in a basin. Also attached with white adhesive resin of some sort. The plumber got the plug out and all the resin off despite the fact it was as hard as concrete. I didn’t watch them work but I know they also didn’t use power tools (I’d have heard).
30 mins later they had a fresh drain fitted and fresh resin in place.
So I’d ask a plumber or surf YouTube if I was in your shoes.
Have the same fitting in our guest room ensuite.
There’s no need for a hex interface as hand tightening is sufficient (with the rubber seal) to achieve watertightness. All very well until it breaks.
The use of silicone may have been accompanied with overtightening.
If it happened here I’d be at it with the Dremel.
Willy.
Firstly, I’m not a plumber (retired engineer)
I have recently changed my plughole which was the same style as this,ie push rod to allow water to drain, although mine did have a nut on the bottom to pull the plug surround into mastic (I used plumbers putty) to create a seal. I suspect she’s had problems before and the whole thing has just been masticed in place unless there is a nut under all the white gunge. If you think about it there isn’t really any other way to put in a plughole, I replaced mine with a mushroom head spring loaded type which the DIY guy recommended and was very easy to fit. Hope this helps and you manage to replace it for her.
Just seen Willy’s reply and yes that circular nut and rubber seal is what I reckon is under the mastic,
possibly to stop a leak in the past.
Some of these in the past had the top ring (the one in the sink) with the thread on. So you have to somehow hold that top ring in the basin while trying to rotate the protruding piece underneath. They can also have an anti clockwise thread just to add a fun variation. Good luck.
Thanks.
Knowing what is under the silicone is a great help.
With all the silicone on my neighbors sink, it not going to be easy.
You are supposed to use a non-setting mastic to seal in a waste outlet, not silicone, which deteriorates and turns black in the basin. Judging by the chips in the glaze around the waste in your photo, and the use of silicone, I suspect this is a DIY botch. That may be why it has broken too, by being overtightened. Hopefully a properly installed replacement will get her sorted out.
I’ve given up.
She’s going to phone our local electrician up tomorrow.
Apparently he knows a good plumber.
Good on you for trying, you’ve certainly earned your lovely looking cake. A new basin is probably the best bet really.
Doesn’t look like there’s much option other than to ‘hack’ it off!
If it was mine, I’d have hacked it off by now.
But my neighbour is in her 80s, recovering from a heart attack she had a couple of months ago.
I don’t really want to stress her out by wrecking he bathroom basin. 
Might be a bit bonkers, but if you are going to hack/dremmel it off and the taps can be isolated locally and have easily removed/reconnected flexible hoses then taking the taps off and then the basin off the wall might be easier and more comfortable than trying to squirrel around and work underneath it.
