Final answer:
Obligate saprobes cannot adapt to a living host because they specialize in absorbing nutrients from non-living organic matter and are integral agents of decomposition in the ecosystem.
Step-by-step explanation:
The statement that obligate saprobes can adapt to a living host is false. Obligate saprobes are organisms that derive their nutrition from decaying organic matter and are specialized to absorb nutrients from non-living organic matter. They play a critical role in the ecosystem by decomposing dead organisms and recycling nutrients back into the environment, hence they are significant agents of decomposition. These organisms, including many fungus-like protists and bacteria, cannot simply adapt to living inside a host organism for sustenance as they lack the necessary mechanisms to overcome a host's defensive responses and are not adapted to absorb nutrients in such an environment.