What happens when wire touches only negative battery terminal?
In short, absolutely nothing (*).

If you only connect one end, there is no complete circuit and as a result no current can flow.



(*) There may be a small current flow for a very short period, but in all likelihood it will be such a short period and such a small amount of charge that you wouldn't be able the measure it.

The reason for saying this is there will be a very very very tiny capacitance (probably so small it cannot be measured) between the other end of the wire and the other terminal of the battery. This will form a complete circuit which will allow a small amount of current to flow during the transient voltage period when the wire is connected.

But again, it is such a small immeasurable amount that you can effectively consider it irrelevant - cosmic rays would probably cause more current to flow in the wire!