Is there a general rule that innocent third parties (like the innocent accused) are not compensated for losses and expenses occasioned by the criminal process?

The general rule that witnesses and other innocent third parties (like the innocent accused) are not compensated for losses and expenses occasioned by the criminal process exists despite the fact that these costs can be onerous. A witness, for example, may be jailed as a material witness. As it was put in Blair v. United States, 250 U.S. 273 (1919) at 281, "The duty, so onerous at times, yet so necessary to the administration of justice according to the forms and modes established in our system of government ... is subject to mitigation in exceptional circumstances".