Foreigners are 外国人。Can a Japanese person, living in Japan, be referred to as a 内国人？
If you are asking whether the antonym of 外国人 is 内国人, technically I must say yes, except that this term is rarely used. (Generally, the term 内国 now only survives in a few words that were coined in 19th century e.g. 内国郵便 or 内国民待遇.)
A person living in the country of their nationality would be more likely called 自国民 or 自国人 (民 more like the government referring to their nations), or 国民, if there is no confusion from the context. You can also say 同国人, which is what someone calls whoever of the same nationality.
In actual Japanese sphere, which is mostly composed of Japanese nationals, who is not 外国人 is usually called 日本人 or （日本）国民. There is a word 邦人, which is practically only used for Japanese expats.
No, you will always hear about a Japanese person specifically referred to as a 日本人｛にほんじん｝. Similarly, you'll hear about people of specific countries referred to as (country)人｛じん｝.
Note: While 内国人does exist in the dictionary, I doubt you will hear it very often (if ever).