My fiance has been living with me for over three years now, a long with her two kids under 18, she is also receiving ssi/death benefits. Now my question is can I claim her on my taxes without her getting into trouble with over the ssi?

it depends;you can claim an unrelated person as your dependent as a qualifying nonrelative rule only if all of the following conditions are met:

1. She is a US citizen or resident of the US, Canada or Mexico.

2. She is not the Qualifying Child / qualifying relative of another taxpayer.

3. She does not file a joint return with another taxpayer.

4. She lived in your home for the entire tax year.

5. The person had less than the personal exemption amount ($3,900 for 2013) in gross income (excluding only non-taxable Social Security benefits,i.e, SSI/death benefits) for the entire year. Gross income includes all income from all sources before any deductions whatsoever, including normal business expense deductions.
6. Cohabitation is legal where you live.
7. You can prove you paid for more than half of her total support.

Well I'm not sure I fully understand that, my fiance only income is the ssi/death benefits, she receives approximately $8,000 a year. So I should be able to claim her right?

Soc Sec benefits are not subject to income tax , therefore do not count as her gross income aslong as they are a her sole source of income. If the only income she had for the year was her benefits, then she has no gross income at all. As long as you provide more than half her support, you can claim her as a dependent.