I've been looking into ways to restart unfinished fermentation and some sources talk about using a Cake, or yeast cake from previous brews. They also talk about pitching on the cake. I've searched to try and find an explanation but haven't succeded thus far. Can someone enlighten me please?
The cake is referring the yeast the was produced from a previous batch of beer. Yeast reproduces as it ferments the beer. The layer on the bottom of the fermenter is the yeast that grew during fermentation. Some people will brew a batch of beer and pitch it directly onto the cake created from a previous brew. The preferred method would be to wash the yeast and measure the amount used for the proper pitching rate.
If you have a stuck fermentation, try giving the fermenter a swirl to stir the yeast up, and also try warming the fermenter a bit, into the mid to upper 60's but depending on the style.
What is your current gravity reading? What type of beer? All grain or extract? What yeast strain?
The bigger question is WHY fermentation stopped in the first place? Did you pitch enough viable yeast? If not i would pitch some more yeast. Are you fermenting to cold? If so give the fermenter a good stir with a sanitized spoon and put it in a warmer spot.
How are you sure fermentation is stopped? Have you taken a gravity reading? Sometimes vigorous fermentation can end within 24 hours.
If you have hit your desired FG keep the brew on the current year cake for at least 2 weeks to finish some conditioning.
As to your question about using yeast from a previous brew. That is referring to using a yeast starter. Made with yeast from the trub of another brewing session and starting a mini brew with some DME. After that is finished you can pitching the whole thing in and you should have enough viable yeast cells to ferment.