Forced Response to a Convenient Minor Opening?
Playing in North America, I have noticed two main approaches to responding to a convenient minor opening:


Only respond with normal responding strength (usually given as 6 HCP).
Respond with any hand that has an ace, a king, or shortness in the minor opened.


The first is covered by many bidding books, so let us discuss the second.

First of all, you must not respond 1NT without at least 5 HCP; this will lead to disaster, as you have learned. When you are broke, your first priority is to bid a four-card major; if you do not have one and partner has bid 1C, you may bid 1D and pass partner's 1-level rebid (or 2C -- other 2-level bids are reverses and thus forcing).

The real issue comes when partner has opened 1D, and you hold a hand like Jxx xxx x xxxxxx. This is the worst case, and probably the least bad action is to pass and hope that your left-hand opponent comes into the auction. The only alternative is 1NT, but this is a terrible alternative (you must not bid 2C, as this must promise strength).