I think it's important to acknowledge the difficult circumstances parents face. Grieving is a very difficult and long process.
The way the employment insurance benefits work, while the parental benefits end at the end of the week of the death of the child, perhaps it's important to note that the EI benefits are paid on a Sunday-to-Saturday basis, so if the child, unfortunately, dies on a Tuesday, that whole week up to Saturday is still paid. It's just the following week that's no longer paid.