How much time can a person go without wearing partial dentures, before their teeth will possibly change position/s?

Time Frame: You're asking for a specific time frame, and that's too difficult to predict since teeth can shift differently depending on the bite, which ones are missing, tongue forces, and bone support. The sooner you replace the missing teeth the less they would have shifted.

It varies: Weeks to months to years to never depending upon a slew of factors.

One week: Your teeth are important for your dental and general health. They help you chew, swallow, speak, and smile. The loss of any tooth may cause your mouth to shift and your face to look older and effect your digestion. Never go more than one week without wearing removable partials. If you wait longer the partials might not fit any more and a new partial will be required.