Crossword Genius

President died in house abroad (7)

Ross

I believe the answer is:

madison

I'm a little stuck... Click here to teach me more about this clue!

'president' is the definition.
(James Madison, fourth president of the USA)

'died in house abroad' is the wordplay.
I cannot quite see how this works, but
'died' could be 'd' (abbreviation next to the year of someone's death) and 'd' is located in the answer.
The remaining letters 'maison' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for madison that I've seen before include "-- Avenue, New York's advertising district" , "4th president of the US - capital of Wisconsin" , "United States president -- Wisconsin's capital" , "US President - county with bridges" , "dance?" .)

I've seen this clue in The Times.
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