Is there any evolutionary benefit to becoming non infectious minutes after inducing death?
Is this a naturally occurring disease or an engineered disease?
So lets try this:
The pathogen, in this case a yeast, infects the hosts blood. The yeast, as part of its normal metabolism, produces a protein that is sheds and which circulates in the blood stream. We will call this protein Cryptomamillian Coagulating Factor 1 (CCF-1). As CCF-1 circulates in the blood, the kidneys and liver try to flush it. However, over the course of some time period suitable for your plot, the kidneys and liver begin to fail, with jaundice, shortness of breath, etc. being the symptoms. Once liver and kidney failure begin, the CCF-1 protein begins to build rapidly in the blood stream. Shortly there after, concentration of the CCF-1 protein reaches a point where a sudden and complete polymerization of the free protein occurs; essentially, over the course of a few seconds, all the blood in vessels and tissue converts to a semi-solid gel. This gel encases the yeast circulating in the body, rendering it harmless. The body can be handled with out much / any risk of infection. Only removing the gelatin blood, and grinding it up to release the yeast again would be sufficient to infect again. And it could be that the the yeast itself is rendered non-viable immediately when caught-up in the flash polymerization. Your choice.
If this is a natural item, perhaps it is occurring now because this was a yeast naturally occurring in a cold area, that has warmed due to climate change. Migratory birds new to the area due to warmer temps are the vector for the yeast to move into civilization.
Hopefully, you find something you can work with in this nugget.