If you missed a Salat, for a reason, like you slept through it, or you forgot it, or something. Then you can make it up. but, if someone leaves salat altogether, out of laziness or not wanting to make it, then he/she is a kafir.
The Prophet (peace and blessings be upon him) said:
العهد الذي بيننا وبينهم الصلاة، فمن تركها فقد كفر
That which differentiates us from the disbelievers and hypocrites is
our performance of Salat. He who abandons it, becomes a disbeliever
he (peace and blessings be upon him) also said:
إن بين الرجل وبين الشرك والكفر ترك الصلاة
Between a man and disbelief and paganism is the abandonment of Salat
Note: when we talk about abandoning salat altogether, we mean the Fard Salawat.
As for missing one, I am not aware of any punishment, and again there has to be a good excuse, if it was missed on purpose but you still make it up or make the other salat you are not abandoning the salat altogether, and when you abandon it altogether that is when you become a kafir, and Allah knows best. As for the evidence to support the punishment mentioned in your question, I do not know any authentic Hadith that supports it, but such a hadith may or may not exist. If you are told this then I suggest you ask for the proof, and it's authenticity.
I am not aware of a hadith which mentions a certain/specific punishment if you miss a salat, I am aware though of the hadith which says::
الَّذِي تَفُوتُهُ صَلاَةُ الْعَصْرِ فَكَأَنَّمَا وُتِرَ أَهْلَهُ
The one who misses 'Asr prayer, it is as if he has been robbed of his
family and his wealth
For more information you may listing to this discussion of two scholars.