There are two cases to consider:
1) Company B buys the shares of company A, but keeps A as a separate entity, a $100$% subsidiary. The individual Balance Sheets here will be
COMPANY B
\begin{array} {| r | r | r |}
\hline
\hline
\text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
\hline
\text{Goodwill} & 10 & \text{Equity} & 10\\
\text{Participations} & 50 & \text {Debt} & 50\\
\hline
\text {TOTAL ASSETS} & 60 & \text{TOTAL LIABILITIES} & 60\\
\hline
\end{array}
The overall value has not changed, only the composition of the Assets. Nothing changes in the Balance Sheet of Company A - it was not a party in the transaction, its shares was the object of the transaction
COMPANY A
\begin{array} {| r | r | r |}
\hline
\hline
\text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
\hline
\text{Assets} & 100 & \text{Equity} & 50\\
\text{} & & \text {Debt} & 50\\
\hline
\text {TOTAL ASSETS} & 100 & \text{TOTAL LIABILITIES} & 100\\
\hline
\end{array}
but what is interesting here is the Consolidated Accounts, the two companies viewed as one from a financial point of view, even though for legal and other purposes they are separate entities. Here we have
GROUP BALANCE SHEET
\begin{array} {| r | r | r |}
\hline
\hline
\text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
\hline
\text{Assets} & 100 & \text{Equity} & 0\\
& & \text {Debt} & 100\\
\hline
\text {TOTAL ASSETS} & 100 & \text{TOTAL LIABILITIES} & 100\\
\hline
\end{array}
How come? First, Debts of both companies are owed to Third Parties, so their amount doesn't change. So Group Debts = 100. Second, The Assets held by mother company B are "internal" - the shares of company A (face value and premium), so they are ignored, "written off" in the consolidated accounts. What Assets remain are those held by company A. So Group Assets = 100. We are then led to find that Group Equity is zero... which is correct, because if we write off Assets we have to write off an equal amount from the other side, of Equity.
Can we arrive at zero by some other road of reasoning?
Well, the two Equity figures add up to \$60. Hmmm, and how much did you pay Third Parties to leave company A? \$60. What Equity was injected into the Group, exited as payment to Third Parties for the buyout. This is why Group Equity ended up zero.
2) Company B bought the shares of company A, but then merged with it. In this case we don't have individual and Consolidated Statements, only one Balance Sheet, which is the same as the Consolidated BS in the previous case.
Leveraged Buyout indeed.