They burst. That's the end of it — a staph cell sitting in penicillin swells and splits at the seam. The wall around a bacterium isn't a finished thing; it's being stitched shut all the time as the cell grows, and penicillin blocks the stitch. Water keeps coming in, the bag keeps filling, nothing holds it. Which means it only works on bugs that are busy growing, and it leaves our own cells alone, because we don't build walls like that.
Fleming didn't know any of that in 1928. He came back from holiday, found a mould on a plate and a clear halo round it where the staphylococci had died, and he didn't tip it into the sink. I would have. I was brisk with the washing-up in my lab days, and I've wondered since what went down the drain. There's a photograph of him years later, white-haired, bow tie, swivel chair, holding a little stack of culture dishes and looking down at them rather carefully.
Ada, the washing-up instinct cost less than you'd think — Fleming later handed out little mounted discs of the mould as souvenirs, signed, and one of them went at auction a few years back for something like fourteen thousand pounds. (Rather a lot for something he'd have called a contaminated plate in 1928.) Best thing anyone ever didn't rinse.
Ada, the spore likely drifted up from the mycology lab a floor below — someone downstairs growing Penicillium for allergy work, a stairwell, an open window. A fungus doing what fungi do, which is get everywhere and be unimpressed by our tidiness.