The subject is still चूहा.
The usual SOV sentence 'एक चूहा घर के बाहर है' would mean 'A rat is outside the house'.
When you want to decrease the emphasis from the subject, English uses the expletive construction 'There is'. In Hindi we accomplish the same by switching the word order. So, घर के बाहर एक चूहा है' would mean 'There is a rat outside the house'.
Because "घर के बाहर एक चुहाँ है" is used when you are telling someone that there is a rat outside the house and you will use "चुहाँ घरके बाहर है" in a situation where you are answering someone's question, like "where is the rat ?" Means that sentence can only use for informing or answering someone