Here is the Greek for Matthew 18:34
[![enter image description here][1]][1]

... which says:
>Then being enraged, his lord surrendered him to the tormentors, until such time as he should repay the entire debt.

There is no mention of "jail/jailers", here. The man's lord intended to surrender him to "the tormentors". These were the ones he threatened him with in the first place, back in verse 25 -- those to who he would be sold. Here is the Greek:

[![enter image description here][2]][2]

... which says:
>But, not having of himself *the means* to repay, the lord commanded that he be sold, with the wife and the children and all his possessions, and so to be repaid.

The lord's repayment at that time would have been settled by the price of the man, his wife, his children and all his goods.

The only mention of "jail" is by the wretched servant in his words to his fellow servant. Here is the Greek:
[![enter image description here][3]][3]

... which says:
>However, the man had no such desire. Instead, when he left he threw him into prison until such time as he might pay back the debt that was owed. 

The Greek word *φυλακὴν*,<sup>2</sup> given as "prison", is what the wicked servant had in mind for his debtor. It was he, not the lord, who had given no thought to how one could repay while incarcerated.

Greek has a word which is given in English as "jailer" (δεσμοφύλαξ <sup>2</sup>), and it is has nothing to do with the word used by the man's lord (*βασανισταῖς* <sup>3</sup>). The "tormentors" in the lord's mind were those who operated labour-camps, and he would be repaid by the wicked man's forced labour over time, not by imprisonment.

>Debt collection has been around as long as there has been debt and goes back to the ancient civilisations, starting in Sumer in 3000 BC. In these civilisations if a debt was owed that could not be paid back, the debtor and his wife, children or servants were forced into "debt slavery", until the creditor recouped losses via their physical labour.  
-- [Debt Collection][4] (Wikipedia) 

<hr>
**Notes:**

1. [Strong's G5438](https://www.blueletterbible.org/lang/Lexicon/Lexicon.cfm?strongs=G5438&t=KJV) - phylakē

1. [Strong's G1200](https://www.blueletterbible.org/lang/Lexicon/Lexicon.cfm?strongs=G1200&t=KJV) - desmophylax

1. [Strong's G930](https://www.blueletterbible.org/lang/Lexicon/Lexicon.cfm?strongs=G930&t=KJV) - basanistēs.  
This word occurs only once in the NT, here in Matthew 18. The definition given by Thayer (et al.) doesn't fit this scenario at all. There is no "truth" to be extracted from the wicked servant, but repayment of a debt, which could only achieved by the man's forced labour -- those to whom the lord was going to sell the servant in the first instance.

  The word should have a more generic meaning that fits a broader use. I would suggest, *βασανισταῖς* describe any agents whose hearts are not inclined towards mercy. Men like the wicked servant, himself.

  [1]: https://i.sstatic.net/hg28Z.png
  [2]: https://i.sstatic.net/5JM1Q.png
  [3]: https://i.sstatic.net/QGlzR.png
  [4]: https://en.wikipedia.org/wiki/Debt_collection#History