Yes, you can borrow against life insurance if you have whole life insurance or permanent insurance. If you borrow against a whole life policy the amount that you borrow will be deducted from the full payout of the policy upon your death. So if you have a $30,000 policy and borrow $1,000 your policy will pay out $29,000 at most to your beneficiary upon your death. Generally interest is added to loan to promote repayment. Generally, you repay a life insurance policy loan while insured is still alive.
How much you can borrow is determined by how long and how much you have paid into the policy. For instance you cannot take out a $10,000 policy and then take a $5,000 loan out on it the next day. The amount you can borrow from these policies grows over time as you have paid more into them. Your policy should come with a breakdown of how much you can borrow from the policy. This amount is referred to as the cash value of the policy.