A quick calculation demonstrates thus:
1. Sun= 1 Solar Mass (1 SM)
2. If ejecta is 10% of SM as sun goes into red gaint (0.1 SM)
3. Jupiter approx 1/1048 SM (0.000954 SM)
4. Brown dwarf as having 80 Jupiter mass or 80/1048 SM (0.0763 SM)
5. Therefore Jupiter needs another 79 times its current mass (0.0754 SM) to achieve brown dwarf status.
6. This would require Jupiter to have caputred 75.4% of the sun's ejecta. This is not very likely due to the orbit of Jupiter and the speed of ejecta.
Conclusion: Highly unlikely.
Assumption: Does not account mass of inner planets and their moons, asteriods etc should they be destroyed by the ejecta and somehow captured by Jupiter's gravity.
