alternatively, in cases of debts, a demand letter can be called a ‘default notice’ or ‘notice of default’.

See:

https://en.wikipedia.org/wiki/Demand_letter

http://www.thelawinsider.com/insider-tips/how-to-write-a-dem...

http://www.duhaime.org/LegalDictionary/D/DemandLetter.aspx

and

http://iva.cleardebts.co.uk/what_is_default_notice.html

https://www.checkmyfile.com/jargon/notice-of-default.htm


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Note added at 2 hrs (2017-04-10 13:17:24 GMT)
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These meanings of ‘εξώδικο’ are confirmed by the Σταμέλος – Χατζημανώλη Λεξικό Νομικών Ορών.

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Note added at 2 hrs (2017-04-10 13:35:59 GMT)
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However, if an ΄’εξώδικο’ is the first step of a lawsuit. it is called ‘a statement of claim’.

See:

https://en.oxforddictionaries.com/definition/statement_of_cl...

http://dictionary.cambridge.org/dictionary/english/statement...

http://legal-dictionary.thefreedictionary.com/statement of c...


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Note added at 3 hrs (2017-04-10 14:07:00 GMT)
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In your type of sentence, one would write, "....otherwise, it proceeds to order a letter of demand to be sent (or served) to the debtor". Usually, a letter of demand is written by a lawyer, so it would be conceivable for someone 'to order a letter of demand' from a lawyer or law firm.

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Note added at 3 hrs (2017-04-10 14:13:10 GMT)
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Alternatively, you could say. "....otherwise it proceeds to instruct its legal department to send the debtor a letter of demand (or a statement of claim)".

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Note added at 1 day42 mins (2017-04-11 11:21:28 GMT)
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After giving this more thought since yesterday afternoon, although it is conceivable that a member of a service could place an ‘order for a demand letter (or a statement of claim) to be sent to a debtor’ to its lawyers or legal department, it would be more common for a member of a service ‘to instruct or request its lawyer or legal department to send a demand letter (or a statement of claim) to a debtor’.