Sometimes participles in the present, perfect or future are linked with nouns or pronouns in the ablative case. This is called the ablative absolute because, firstly, this type of phrase is always in the ablative case, and secondly, the phrase stands alone and is completely independent of any grammatical constraints of the main sentence it is linked to.
Such a clause can be translated in various ways, for example with the words ‘because’, ‘when’, ‘after’, ‘although’ or ‘if’. In this example the ablative absolute phrase could be perhaps translated most naturally as ‘after my debts have been paid’.
The verb ‘to be’ does not have a participle and therefore such a participle does not appear in sentences where you would expect it.