Are negative coupon bonds possible?

The rule is, no, negative coupons don't exist.

For the exception to the rule, Reuters found a couple of cases in history where bondholders paid a coupon:

PRACTICAL PROBLEMS

Data from IFR shows a range of issuers including cities, banks and companies have bonds with theoretical negative coupons.

These are unlikely to ever be imposed, though, as market infrastructure is not set up to collect coupon payments from multiple investors to an issuer.

Europe’s main clearing houses, Euroclear and Clearstream, which settle bond deals in the region, have said they will not accept any debt which has a fixed negative interest rate.

On floating rate notes, they said negative coupons have usually paid zero because the issuer set a floor, chose not to collect due to the burden, or the bond terms did not allow for a payment to be made.

Matthew Hartley, a capital markets partner at lawyers Allen & Overy, said bond terms would not normally allow cash to flow from investors to an issuer.

“It is very difficult to enforce against what is in theory an anonymous mass of bondholders,” Hartley said.

This has still created uncertainty among investors though. Allen & Overy said it has helped more issuers insert explicit terms in bond documents flooring coupon rates at zero in recent years.

STRANGE EXCEPTIONS

There are some examples where negative coupons were paid.

Euroclear said it has on a few occasions collected coupon payments due from investors to issuers on short-term French commercial paper known as titres de creances negociables (TCNs). This paper is usually only held by a couple of investors so payments are easier to collect.

Going back 14 years, Warren Buffett’s Berkshire Hathaway issued a bond with an effective negative coupon in 2002. This was sold with a warrant to buy Berkshire shares, the net effect of which was investors paid more in interest than they received.

Yes, but they're annuities, so they aren't "true" negative coupon bonds.

In August 2019 the 3rd biggest Danish bank Jyske Bank issued a series of 10 year mortgage bonds with a -0.5% coupon. This had to happen since fixed rate mortgage bonds have to be issued below par according to Danish law. But since the negative coupon is just subtracted from the principal payments, the payments are still going to the bondholders every quarter.

See the following article for more information: http://news.coveredbondreport.com/2019/08/annuity-structure-allows-jyske-negative-coupon-milestone/