I definitely recommend calling the Assessor's office in the county of the property - to get the precise answers. But from what I know:
1. It's likely the death was never reported to the county back in 2003. So technically no one is aware that one of the owners is deceased and therefore their name still appeared on the deed in 2013.
2. The new ownership depends on how the title is vested (i.e., tenants-in-common, joint tenancy, etc). If JT, the other remaining joint tenants inherit the deceased tenant's interest in the property. If TIC, the shares go to whomever are his/her beneficiaries.
3. The only way to receive full 100% ownership is for the remaining owner and possibly the deceased owner's beneficiaries to deed their shares to your friend.
Ultimately paying all the taxes doesn't constitute full ownership. The first thing that needs to happen is reporting the death by filing the appropriate paperwork to the county. Know that there's a possibility for the property to be reassessed; if so, you and the remaining owner(s) will have to pay back property taxes for the years going back, but no more than 7 years.