I think new plant is coming up from the seeds which might have fallen on the soil. check out the pic: https://imgur.com/a/3fP6f
Sorry, but I think the little seedlings are just weeds. Basil seedlings even from the seed leaves have much rounder leaves:
Basil does not self seed readily and of course it couldn't have dropped seed unless it bloomed and the flowers remained on the plant for the long time it takes them to make seed and then to finally release it.
Basil is an annual. Its genetic programming is to sprout, grow, bloom, set seed, and die all within a single growing season. If you keep it cut back and don't allow it to bloom, you can extend its life somewhat, but over time it tends to get woody (as yours apparently was) and less productive.
Unfortunately, you didn't do your plant any favors by not harvesting it. What you want to do is not pluck individual leaves but to cut stems back to just above a leaf node. Cutting back helps keep it not only from blooming, but from getting so woody. It rejuvenates it a bit. But even if you had been cutting it back, basil is not a plant you can keep for years.
So yes, I think your plant is dead and past reviving. But that is mostly the course of nature. Start a new one and this time don't be afraid to harvest it (once it is big enough that you are not taking more than a third of its leaves).
Every stem you snip will branch into two at the cut point, so it will get much bushier, with lots more leaves.