Yes I think it's "onion weed" which is a "relative" of aliums but called nothoscordum inodorum. Apart from the seeds you get lots of tiny little bulbils forming which get knocked off when you try to lift it out, and continue growing. Kind of like those weedy oxalis do. You really need to spade well around the plant (and they can settle quite deeply) and lay out on a garbage bag or similar and kind of sift thru to get rid of the babies - or dump the whole clump and replace the soil. Weed killer while active may help.

Here is a link that might be useful: onion weed

I agree with Alisonoz, I've been plagued with that over the years but never let it set flower. I found the only thing that worked was a 12 months weed killer, glyphosate (Round-up, Zero 490, whartever) did no more than give it a shock for a month or two. Once established, very hard to get rid of. Some experts will tell you to simply sell up and move!