some of the slime molds may possibly have fossil existence. for details please read the article of Retallak et al., 2013
Retallack, Gregory J. "Comment on “Trace fossil evidence for Ediacaran bilaterian animals with complex behaviors” by Chen et al.[Precambrian Res. 224 (2013) 690-701]." Precambrian Research (2013).
Well ,slime molds have a very poor fossil record ,there are only two occurences of fossilised slime molds found from phanerozoic rocks,both in baltic amber (Eocene in age; Dorfelt et al.2003).For further information please refer this book,it may help you to find out your answer.Have a Good Day