Even that couldn't be guaranteed to finish off the little pests. Allium related plants, such as garlic, chives and others can readily take over an entire garden, as I can personally attest.
OK, so you can dig 'em up or you can cover them with a sheet of black plastic covered by a few more layers of newsprint. Leave it covered for up to 6 weeks and it should all be dead. If you catch it this time of year (Spring) and it's green or even flowering, Round-up works pretty good. Nice thin about round-up is it won't leave harmful residue in the soil. But be sure to use it only on calm wind days... if it drifts on to lawn grass or desirable flowers you can kiss them good bye.
If you decide to try digging them up, purchase a good pair of reading glasses since you'll need to seek and destroy even the smallest tendril of the rhizome like root structure. Leave even one and you'll be back with shovel in hand before the end of summer...
Best of luck!