When someone dies, the person that they chose before hand to be the beneficiary, inherits the IRA.
The taxable distributions to the beneficiary have to be included in their gross income.
Treat the IRA as your own
If you are the spouse and have inherited a Traditional IRA, you can treat it as your own.
You will have to designate yourself as the account owner or...
Roll the Traditional IRA into your IRA.
You can also leave it as is and remain the beneficiary.
If you make contributions including rollover contributions to the IRA, and you don't take out the minimum required distribution for the year, you will be considered to be treating it as your own, but you must be the sole beneficiary of the IRA, and have unlimited rights to withdrawal from it.