The story concept
After one accidental swallow, a pink gum character moves into an imaginary apartment, throws bubble parties, and watches calendar pages fly. That scene is invented for the joke.
What the sources actually say
Mayo Clinic says the body cannot digest the gum base, but swallowed gum does not stay in the stomach. A piece generally moves relatively intact through the digestive system and leaves in stool. Cleveland Clinic likewise rejects the seven-year claim.
Where the evidence stops
The usual outcome for an occasional piece does not make swallowing gum a good habit. Mayo Clinic notes that, very rarely, large amounts of gum combined with constipation have blocked children's intestines. This video does not diagnose a person who swallowed gum or promise the same transit time for everyone.
The useful takeaway
Put used gum in a wrapper or trash can. If someone has swallowed a large amount and develops concerning symptoms, seek medical advice.