I don't know about "stellar" cells; what comes closest are BL21(DE3)Star cells, which feature a slower degradation of mRNA. As to starting a new batch, you can use a tube from the old batch without problem. There will be many generations of growth in fresh medium until you process the cells to make a new batch.

Thanks Pierre!

Except for trying to understand what is the difference between those cell types, I was wondering if there might be something special about cells coming from a commercial manufacturer (vs "Home made" cells), perhaps making them unusable as a starter for a new lab grown batch

These are the stellar calls:

https://www.takarabio.com/products/cloning/competent-cells/stellar-chemically-competent-cells