To reproduce:
1. Open attached project
2. Open test scene
3. Press play
4. Hear the last targetLength samples of the clip
5. Stop scene
6. Disable Stereo game object and enable Mono
7. Press play
8. Wrapped samples seem to be wrongly offset, resulting in the first samples of the clip being heard at the end of the new grabbed data

Resolved (Not Reproducible):

The script is computing the buffer offset incorrectly. The GetData API works in sample frames (left+right) while the C# array works on single samples and therefore needs to be multiplied by the channel count. Here's a fixed version:

using UnityEngine;
using System.Collections;

[ RequireComponent( typeof( AudioSource ) ) ]
public class WrapMonoBug : MonoBehaviour
{
// Only mono clips seem to trigger the bug
public AudioClip clip;

// Use this for initialization
void Start ()
{
int bufLength = 16384;
int targetLength = 15000;

float[] buf1, buf2;

buf1 = new float[ bufLength * clip.channels ];
buf2 = new float[ targetLength * clip.channels ];

int offset = clip.samples - targetLength; //grab the last targetLength samples of the clip.
clip.GetData( buf1, offset ); // Probably a wrap error here in GetData: after wrapping, it seems offset in the target buffer is incorrectly updated

System.Array.Copy( buf1, buf2, targetLength * clip.channels ); //copy to new buffer( to set data in a new clip )

AudioClip newClip = AudioClip.Create( "test", targetLength, clip.channels, clip.frequency, false); //create new clip of targetLength and set data
newClip.SetData( buf2, 0 );

//play result: we hear the attack of the original clip instead of only the targetLength last samples
AudioSource source = this.GetComponent< AudioSource >();
source.clip = newClip;
source.loop = true;
source.Play();
}
}