Literally a "Bad luck".
The this- prefix frequently denotes something undesirable - in this case the phrase equates to the English phrase "road accident".
These may also be describes as trochaia (pl.).
Thisdichimata (pl.) are common occurrences in Cyprus, indeed there is hardly a five-mile stretch of thromos (road) anywhere on the island not decorated by sad little crosses, wreaths and small wayside shrines to individuals who finally came to terms with the realization of their own mortality - however briefly.
Possibly in an attempt to come to terms with this, or else an attempt to avoid coming to terms with this prior to fatality, post Thisdichima behaviour has been somewhat ritualized. (Unless those involved just ignore the accident and drive on to avoid paying on their insurance if they have any.)
1. If still alive and capable, both parties leap from their cars, glaring in disbelief at the bent metal and the culprit as if daring them not to be to blame. Insults may be screamed from a safe distance without making eye contact unless one of the parties believes you cannot harm him whereupon he may become violent.
DO NOT offer insurance documents at this stage. It will be taken as either weakness or an admission of guilt and may precipitate verbal or actual violence.
2. Stalk around the periphery of the accident snarling into your mobile phone to demonstrate the vital multiple appointments you are now forced into cancelling due to your opposite number's clumsiness. Call the police whilst you are at it to get your story in first, but do not snarl at them. Bear in mind they will not show up.
3. If there is any possibility of your being to blame or else blamed, collapse at the roadside. Your removal to the Nosogomieon, preferably by ambulance, gives you a moral advantage over your still ambulant competitor.
4. Women at this point collapse into either hysterics or tears. It is permissible to scream about nearly killing your children whether they were actually in the car or not.
5. Any minor injuries should be exaggerated.
Do not confuse responsibility with the legal concept of blame, especially if the policeman is related to your your opposite number but not to you.