Assuming the bond was actually issued with a negative coupon, if you are short (borrowing someone else's bond to sell the bond at a lower price / higher yield)
Who pays the coupon?
There are at least three parties here, the issuer, the owner, the short seller, and I'm at a loss for who is getting money from who at coupon payment time
Negative coupons are not the same as a negative yield.
A $1000 bond that you purchase, at a premium, for $2100 that produces 10 annual coupons of $100 and a redemption of $1000 has a real, positive coupon ($100). The holder of the bond gets this coupon, and the maturity value
However, you get back less than your initial investment. There is no growth; the original investment shrinks, or has a negative growth rate. Most mortgage or bond calculators choke on this situation...
The assumption that bonds have been issued with a negative coupon is not correct, or at least is has not occurred thus far. We'll look at this future possibility in the final paragraph. For now, lets look at the current bond market. The issuance of government bonds which carry a negative gross redemption yield is the result of governments issuing bonds at an issue price which exceed the nominal/redemption price and any coupon yield receivable over the life of the bond. I can find no instances of bonds with a negative coupon, though many have tiny positive coupon yields.
The short seller of a bond with a negative gross redemption yield will be liable to pay the buyer the interest amount determined by the coupon. If the short seller has borrowed the bonds in order to sell them, then the short seller will receive the interest due from the lender to offset the interest paid to the buyer. If the short seller has not borrowed the bonds, but has sold them using some sort of synthetic contract such as a Contract for Difference, then the short seller will pay the coupon without receiving any offsetting payment.
I thought this was an interesting question and it will be interesting to see if, at some time in the future, governments do ever issue bonds with a negative coupon. To date, this does not appear to have happened.
So what would happen if we assume that a government issues a bond with a negative coupon. The buyer of the bond would be required to pay the equivalent yield to the government according to the bond contract specification. If an investor sells short such a bond, they would then become entitled to receive the interest from the buyer. If they have borrowed the bonds in order to sell them short, then they would pay any interest received back to the lender - this chain should eventually end with the ultimate owner/lender paying the government their dues. If they have sold short using a synthetic contract, then presumably they would keep the interest from themselves.
The issuer pays (negative money in this case) to the holder. The person you sold your borrowed bond to gets this (negative) amount. The person who you lent you the bond is eligible for that (negative) payment, they were the original holder of the bond. When you return the bond you thus have to compensate the original holder. Now turn around the cash flows and you're there.
The new holder pays the issuer, the original holder pays you.
