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I am sorry to hear about the way you feel at the moment. From your description I understand that you are talking about a specific person who lies even about their heath. Depending on circumstances, lying usually affects the sense of trust we have towards someone. Trust is one of the most important thing in a relationship and if trust is "damaged" then the relationships be comes very complicated and problematic. This behavior can also affect someone's self esteem as they could be involved in checking behaviors (e.g. checking mobiles, correspondence, stalking) which may reinforce paranoid ideation and this in turn reinforces more checking and questioning which can often lead to many arguments. Self esteem can also be affected in terms of one questioning one's self value or appearance or intelligence etc. Also, a person can start to question theme selves and this may alter the person's perception of the truth and reality, trigger guilt feelings and ultimately prevent the person from making the right decision for themselves.
Obviously I do not know a lot about the person you are describing and whether he does lie about his health condition or not. However, I would advise you to follow your instinct and if you feel that there is a pattern of lie that he follows generally about himself either to attract attention or elicit sympathy or even assistance, financial or other then the best thing for you would be to leave this relationship. A statement like "I am dying" could be easily confirmed if you spoke to a family member of his. Generally speaking I would not advise you to start checking his personal staff to find proof. If you feel that he is not benefiting in any way by his statement to you that he is dying then this may true. So it would be best if you kept some distance and continue as normal the relationship without giving any notice or importance to his illness. If you feel that he keeps bringing it up because he has some benefit from this then this should be alarming. Also, do not forget that certain people have a disorder of being pathological liars and create all sorts of stories in a need to elicit admiration and attention. Your instinct and logic should be able to tell you who you are dealing with and what would be the best decision for you.
I hope that helps
Please feel free to share any feedback on these thoughts
All the best