Any letter which is not pronounced can be described as e.g. "silent T".

In French the last letter of a word is usually not pronounced except when the next word starts with a vowel but this exception would not apply in English to loanwords of French origin so there are loanwords in English where the final T is never pronounced - e.g. parfait.       

I am told that in American English there is a phenomenon known as an "unreleased T" which means that whether on not the T is fully pronounced depends on whether the speaker wishes to emphasise the word (T not normally fully pronounced but can be pronounced fully for emphasis) and that this might be what the OP is referring to. In British English we just use tone and speed for emphasis but do not change pronunciation so, absent this phenomenon, this would be regarded in British English as a fault and we refer to it by saying e.g. "he drops his Ts".