You didn't say how the deceased parent made $6,000. If the deceased parent had $400 or more of business or self-employment income, a tax return must be filed. A tax return also must be filed, regardless of income, if the deceased parent received advance premium tax credit for health insurance from the Marketplace ("Obamacare"), or if the deceased parent took money out of a Health Savings Account (HSA) or Medical Savings Account (MSA).
If a tax return is required, the executor or administrator of the deceased parent's estate is responsible for filing the tax return. If there is no executor or administrator, then one of the deceased parent's children should file the tax return.