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I agree with DjiNN - to convert the FWD Corolla to an AWD with off the shelf components from other Toyotas - would be a monumental undertaking, to say the least.
Has it been done - sure. Was it worth it - depends on whom you ask. Fensport UK is one example - took a 9th gen Corolla and swapped the AWD from the Celica GT4. Something to the tune of well over $40K initially, and they are a full garage that deals with Toyota modification (they also did a 7th gen Celica AWD).
If you are doing this for experience and have access to a garage, fabrication equipment, and pile of parts (whole donor RAV4 or AWD Matrix or similar) - I'd say go for it. Even for a hardcore DIYer with nearly an unlimited budget - this is a huge project. Depending on where you live, might not even be able to register the car for highway use - which makes it a track-only car or expensive paperweight.
If the car was a body on frame instead of a unitbody and/or if Toyota also released an 8th gen Corolla with AWD - then I could see this possibly being a DIY-able project. As most of the powertrain can be modified significantly without affecting the base vehicle. As it stands, not enough parts exist to allow for a drop in swap - fabrication required to "make" the other COTS parts fit is non-trivial.
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2002 Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Matrix XRS, 2.4L 2AZ-FE VVT-i
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