Is there any examples of information-theoretic secure MPC for dishonest majority against malicious adversary?

What you are asking for is not possible, not even if you ask for passive security. Here is a sketch of a proof.

Suppose for sake of contradiction you have an $n$-party MPC protocol $Pi$ for $f(x_1, ldots, x_n) = x_1 land x_n$, where the $x_i$'s are bits. This protocol is secure against a computationally unbounded adversary who can passively corrupt $ge n/2$ parties.

You can take this $n$-party protocol $Pi$ and construct a related 2-party protocol $Pi^*$. Player 1 in $Pi^*$ plays the role of parties 1 through $n/2$ in $Pi$, and Player 2 in $Pi^*$ plays the role of parties $n/2+1$ through $n$ in $Pi$. So $Pi^*$ is a 2 party protocol that takes input $x_1$ for Party 1 and $x_n$ for Party 2 and computes $x_1 land x_n$.

The 2-party protocol $Pi^*$ is secure against 1 corrupt party. Corrupting 1 party in $Pi^*$ is like simultaneously corrupting $n/2$ parties in $Pi$, and by our assumption $Pi$ is secure in that scenario.

So now we have a 2-party protocol $Pi^*$ for securely computing the AND of two bits, which is secure against a passive, computationally unbounded adversary (who corrupts 1 party). But this is known to be impossible. If you're asking about perfect security, it was proven in:

• Kushilevitz: Privacy and Communication Complexity

The proof was later generalized to statistical security in:

• Maji, Prabhakaran, Rosulek: Complexity of Multiparty Computation Problems: The Case of 2-Party Symmetric Secure Function Evaluation, section 4