Yes puffers can release toxins when they die, if they arent removed asap. I had a 14in stars and stripes puffer die, that i had for about 6 years, and i bought him at about 5in. He just mysteriously stopped eating, became very sluggish, and about a day later when i was viewing my aquarium he spazzed out from laying on the substrate and a few minutes later died ... I doubt it was old age, but i dont know what the other causes may be ...
But since i got another S & S puffer and have had him now for a few years; (now at 7inches) ...
And i also had a relative that has a 240gal agressive system with an 8in golden. He had went away for 2 days. The night he left the housekeeper called and said it didnt look normal and was not moving from its "rest spot", he didnt think much of it - a day later he arrived home with a total tank wipeout ..... When all fish but the puffer looked normal and ate/swam fine !!
I know that the 2 top killers of puffer are internal "worms", and the extensive use of copper medications on a tank containing a puffer :[