With the death of President Karimov, Uzbek can expect to see an improvement in the country's human rights. Karimov, a former soviet, has spent the last 25 years ruling his country with an iron fist, crushing those who sought to criticize his administration. With no clear successor in place, the Uzbek people can now appoint a leader who can make improvements in their lives, starting with human rights.
I believe human rights will improve in that country only for two reasons. The most prioritized would be, those whose human rights have been breached band together and seek their rights in almost any way possible. I am positive each will endure suffering but their cause is just. The second priority would be that the living and whom replace the dead be held responsible for their wrong thinking.
Although the leader of a country has died, human rights won't necessarily improve because there was probably a motion in place to carry on the regime. That means things will probably stay the same as they have been. If there's a public political overhaul, it is doubtful that human rights would improve.
Uzbek's human rights are unlikely to improve just because the recent president died. Uzbek needs a completely different type of government - a government that respects civil liberties and defends individual rights. Unfortunately, many countries like Uzbek use brute force to govern their citizens. This is unlikely to change until a totally different government comes to power.