I'm going to assume that you meant each unit cost you $10 (not $1 as you stated; 100 units @ $10 each = $1,000).  That being said and using your example:

You would report gross sales of $10,000.

You would report Cost of Goods Sold of $500:  The 50 units you sold at a cost of $10 each.  The formula for Cost of Goods Sold is:  Beginning inventory + purchases - Ending Inventory = Cost of Goods Sold.  In your example, Beginning inventory = 0, purchases = $1,000, Ending inventory = $500, so COGS = $500.

Your gross profit would be $9,500 and that is what you would report on your tax return.  From this you would subtract any and all business expenses to arrive at your net income which is what you tax would be based on.

Technically, inventory is NOT an expense.  It is an investment that gets written off when you sell it.  It is charged to Cost of Goods Sold when you sell it.

If you are required to present a Balance Sheet in Schedule L for the year, you would show the remaining 50 units as inventory valued at $500.

So let's say I had $10,000 in profit and 0 inventory on the last day of the year, December 31st. On that day if I spent the $10,000 to buy more inventory to resale, my profit for that year would be $0 if I had no more sales on that last day. So then I wouldn't be liable for any taxes for that year since I purchased the inventory but for the next year when I sell it and profit from it then I would be held liable to pay for it for that years tax return (unless we have more costs then profits)?

No ... the inventory cost is taken into consideration only when it is sold not bought if you are using the COGS inventory method.