Well, these are nominal yields, so it's unlikely that they go properly negative. However, it has happened before and, in theory, can happen again. 3m bills, for instance, did trade negative during the height of the '08 crisis. In Japan and Switzerland negative money-mkt rates have also been observed at times in the past.Quote from tradingjournals:
Big D, Martinghoul and others: Is it possible that the yield of the 2's get negative? I am asking because I just found out that I got filled on an order I did not cancel on the 2's that was at 109'225, and I want to double check whether the assumption of positive yield is something I should count on? If yes, I can take the risk of a 1% rise that would result from a zero yield.
One thing to think about is that the price of the futures may rise more or less than 1% implied by the move in the yield of the 2y bond. Especially, in an environment where 2y yields approach 0% and there's all sorts of balance sheet constraints, which can cause the basis to trade all over the place.
