One cannot be jailed as you described.
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One of my colleagues mentioned that a person can be thrown in jail for not paying child support. This happens quite often, sadly. This particular matter, and others, like failure to pay other kinds of court-ordered payments, are usually handled as civil contempt matters.
Child support, in particular, is a tricky one. Back payments are not discharged, regardless of changed circumstances. It is expected that a person paying child support will go to court to file for a modification of a child support order if s/he loses his/her job or is reduced to part-time employment or something similar.
It is routine in DC for a judge to issue an arrest warrant for somebody who has not paid court-ordered fines or contributions in criminal cases. The expectation is always that a person understands his/her obligation to make court-ordered payments and will take the initiative to go back to court if s/he is not able to make the payments. If a person doesn't do so and s/he is picked up, the matter is handled as an issue of contempt of court, which is not a right protected by the Constitution.
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