Can bond yield become negative? Yes 2015-2017 many bonds traded at negative yield. https://www.ft.com/content/312f0a8c-0094-11e6-ac98-3c15a1aa2e62 shows a realistic example of a vanilla bond trading at $104. Yield is negative –You pay $104 now and will get $100 repayment so you are guaranteed to lose money.
Mathematically, when yield approaches negative 100 bps, price goes to infinity.
When yield approaches zero, bond price would go to the arithmetic sum of all coupons + repayment.