That is a good question. You'd look at a price/yield curve and think hey, this is asymptotic, going to infinity as it gets near zero.
But I suppose not. Would be interesting to know, though.
If a bond yield drop from 2% to 1% (-50%) causes a bond to rise from 100 to 150 (50%), would a follow on drop from 1% to 0.5% result in a rise from 150 to 225, both 50% again?
Obviously it can't, because so many in the world have flipped to being negative interest rates.
Some rough calculations...
Consider a $1000 30-year bond with a 2% coupon. It pays out $20 per year, or $600 over the lifetime of the bond. So the value of the bond is $1600 after 30 years (ignoring compounding -- reasonable for such a low interest rate).
The day after you bought it, the yield plummets to 1%. Someone buying a $1000 30-year bond that day would be getting $10 a year for 30 years, or $300, giving a 1% bond a future value of $1300. In other words, it will be worth 1.3 times its cost in 30 years. That person might also consider buying your bond. It would be fair for the second buyer to pay you $1600/1.3 or $1230 for your bond. So that's how much your bond would be worth after the yield plummeted from 2 to 1%. It would go up 23%.
The next day the yield goes down further, to 0.5%. A third buyer of a $1000 bond enter the picture, expecting $5 per year for 30 years, or $150, making the future value of the 0.5% bond equal to $1150. At 1.15 times the cost, the third buyer might offer the second buyer $1300/1.15 or $1130 for the 1% bond. So the second bondholder would see a rise in bond price of 13%. (The third buyer might also buy your 2% bond at $1600/1.15 or $1390, again a 13% increase from the day before.)
If the yield goes to zero, $1000 today would be worth $1000 in 30 years. No growth. So a 2% bond having a future value of $1600 would have a price of $1600 today. A 60% increase over the price it was bought at a few days earlier -- not infinite. The 1% bond would have a price of $1300 and the 0.5% bond would have a price of $1150.
2% to 1% causes the price to go up 23%;
1% to 0.5% causes the price to go up 13%;
0.5% to 0% causes the price to go up 15%;
1% to 0% causes the price to go up 30%.
Craig's comment about 1% 30-year bonds providing little insurance is borne out by these numbers. A stock market drop of 50% would not be compensated by a bond rise of just 30% (assuming yields don't go negative). A 2% bond could go up 60% in such a situation, so it would provide better insurance.