He asked me to talk to Tom rudely.

[navi tasan]

1) She asked me to talk to Tom rudely.
2) She asked me to talk to Tom, rudely

In each case, was I supposed to talk rudely to Tom or was the asking done rudely?

I think both are ambiguous, but the first one would tend to mean that I was supposed to talk rudely to Tom and the second one would tend to mean the asking was done rudely. In the second one 'rudely' seems to have been added on as an afterthought.

The sentences were written by me.

I like to explore the Twilight Zone of the English language and am obsessed with ambiguity.

 

[jutfrank]

I don't think the comma makes any difference.

 

[emsr2d2]

1) She asked me to talk to Tom rudely.
2) She asked me to talk to Tom, rudely.

I would take the first to mean "She asked me to talk in a rude way to Tom". The second is indeed ambiguous. I don't find it very likely with a comma, though. If it was added as an afterthought (regardless of the intended meaning), I'd expect a dash.
The unambiguous way to express that she was rude in the way she asked you is "She rudely asked me to talk to Tom".

 

[jutfrank]

I think I understand the question fully now. You've added a comma because what you're really asking about is how prosody can determine interpretation.

Yes, I think you're right. There's something of a general basic rule about adverb placement where any adverb is assumed to modify locally, i.e., to the closest verb. This is why it's easier, if you're talking about structure alone, to interpret the talking, not the asking, as rude. So for precisely this reason, there has to be some prosodic tactic on the speaker's part to shift that modificaton to the previous verb phrase. This could be done by breaking that local connection with a combination of a pause and a subtle change of intonation on pronouncing the adverb. Obviously, you can't see intonation in a written sentence, but the dislocating pause could be written with a comma or, as I think emsr2d2 is saying, more effectively with a dash, to really help the listener understand something unusual is going on. It's anything but an afterthought—it's a way for the speaker to attempt to get the message across. If it truly were an afterthought, in that the speaker had finished the sentence and then decided to add another modifier, then the prosody would be different again and I don't see how there could be a way to show which verb it were modifying.

 

[Annabel Lee]

2) She asked me to talk to Tom, rudely

In each case, was I supposed to talk rudely to Tom or was the asking done rudely?

I think both are ambiguous, but the first one would tend to mean that I was supposed to talk rudely to Tom and the second one would tend to mean the asking was done rudely. In the second one 'rudely' seems to have been added on as an afterthought.

A third interpretation is possible with (2), namely, that it was a rude request; it was rude of her to ask "me" to talk to Tom.

Compare:

She asked me to sit elsewhere, rudely.​