Yeah depreciation expense should be a negative value on your income statement. It deducts from your revenues to reach your income. Some companies bracket their expenses to show that they're negative or they don't bracket all their expenses and just imply that they are deducted.
Think of things as credit/debit balances. Not as negative and positive. Depreciation expense has a debit balance, and should have a debit balance. There are some exceptions where you may credit an expense like adjusting bonds payable or something.
Typically expenses have debit balances always. As for the Asset, your asset shouldn't be a negative value. If your using straight line, it can only reach 0 at the end of it's lifetime.
If your using double declining balance it will still be positive, it's just when you salvage or trade it, you may have a gain or loss on the transaction. Accumulated amortization on an asset should never be greater than the asset. That wouldn't make sense.
It's like a building Costing you $100,000, and you having accumulated depreciation of $150,000. It's not possible. If you expect the asset to be around longer, you will revise your estimate. You will learn this in Intermediate Accounting.
I am assuming when you say negative thati its increasing net income. Generally, this would not happen however included in this line is usually amortization of intangibles. For instance Value of Business Acquired (VOBA) which is the discounted future profits on business acquired can increase net income as it amortizes. This is because the expected gross profits that is use to amortize are not locked in and are unlocked periodically. If the expectation is that future profits are longer then a negative charge is included in amortization to reset the cumulation amortization taken to date (i.e. increases net income im that period).
There are instances where this may happen so knowing what asset this is depreciating woudl provide more detail in my response.