After I keg, I swirl the remaining contents in the fermenter, wait 5-10 minutes and then fill a sanitized 24 oz jar (spaghetti sauce) all the way up. I put that in the fridge with lid loose. After setting there is about 8-10 oz of yeast slurry which is a lot for my 3 gallon batches.
Next brewday, I usually just decant and pitch the slurry directly into the wort. I usually use the same yeast 2-3 brews in a row, so, the stored yeast never gets very old.
The settlement in my yeast jar has trub, bits of hops, etc. but, it seems to work.
I don't worry about what was brewed before with the yeast. I don't think there is enough matter there to make a difference. Then again, I don't brew extreme hoppy or dark beers, so maybe this is just not a concern for me but could be for others.