user11518: If I let relationships and other things go as a way of embracing detachment then will there be karmic "retribution"  or will it leave some hole that will force me into rebirth?

user295: If you let go mentally then there will be more positive karmic efforts in the future.
If you let go by being attached to an ideal or view or practice or embracing this as a view, ideal or practice then this might cause negative karma for the future depending on how much you get attached to the ideal, view or practice. E.g. if you see many charities which seem to do good but many of the volunteers seem overly attached to the cause. This will have an element of unwholesomeness in it.
So you have to get detached by training your mind than through other means. Also without going overboard with being detached if you practice this to some extent then this also might help towards letting go through your mind but keeping in mind this is a double edge sword. If this is leading to some form of craving or attachment then this is not the right way it should be done, and also will have some negative karmic effect.
For rebirth not to happen you should not get attached at the dying moment. If there is any effective (not dormant or not ahosi) kamma rebirth will happen. Attachment to view, ideals and practices, even to that of detachment, also may have potent for a next birth. If you have mentally let go then there will be not potent karma and there will be no rebirth.
More technically according to dependent arising, rebirth is generated in two sequences:

(1) ignorance (avijjā) + karma -> the stream of consciousness beginning at rebirth (vinnāna).
(2) craving (tanhā) + clinging/fuel (upādāna) -> existence (bhava) + rebirth into that existence (jāti).

Source: Dependent Arising by Piya Tan

user8157: The Buddha did not teach 'kammic-retribution' & 'non-attachment' together. 
'Kammic-retribution' is a moral yet defiled & mundane teaching; based in the ordinary view of 'self'. 
'Non-attachment' is a supramundane/transcendent (lokuttara) teaching; based in not-self (anatta). 
Please refer to MN 117, which distinguishes these matters. 
This being said, any important & essential relationship in life must be looked after, for example, the relationship an enlightened monk must have with laypeople. 
The Buddha taught 'non-attachment' rather than 'detachment'. The advanced Buddhist practitioner learns to have metta without attachment. Having metta will look after/safeguard any relationship. 

11518: <p>If I let relationships and other things go as a way of embracing detachment then will there be karmic "retribution"  or will it leave some hole that will force me into rebirth?</p>
 295: <p>If you let go mentally then there will be more positive karmic efforts in the future.</p>
<p>If you let go by being attached to an ideal or view or practice or embracing this as a view, ideal or practice then this might cause negative karma for the future depending on how much you get attached to the ideal, view or practice. E.g. if you see many charities which seem to do good but many of the volunteers seem overly attached to the cause. This will have an element of unwholesomeness in it.</p>
<p>So you have to get detached by training your mind than through other means. Also without going overboard with being detached if you practice this to some extent then this also might help towards letting go through your mind but keeping in mind this is a double edge sword. If this is leading to some form of craving or attachment then this is not the right way it should be done, and also will have some negative karmic effect.</p>
<p>For rebirth not to happen you should not get attached at the dying moment. If there is any effective (not dormant or not <a href="https://suttacentral.net/define/ahosikamma" rel="nofollow noreferrer">ahosi</a>) kamma rebirth will happen. Attachment to view, ideals and practices, even to that of detachment, also may have potent for a next birth. If you have mentally let go then there will be not potent karma and there will be no rebirth.</p>
<p>More technically according to dependent arising, rebirth is generated in two sequences:</p>
<blockquote>
<p>(1) ignorance (avijjā) + karma -&gt; the stream of consciousness beginning at rebirth (vinnāna).</p>
<p>(2) craving (tanhā) + clinging/fuel (upādāna) -&gt; existence (bhava) + rebirth into that existence (jāti).</p>
</blockquote>
<p>Source: <a href="http://www.themindingcentre.org/dharmafarer/wp-content/uploads/2009/12/5.16-Dependent-arising-piya.pdf" rel="nofollow noreferrer">Dependent Arising</a> by Piya Tan</p>
 8157: <p>The Buddha did not teach 'kammic-retribution' &amp; 'non-attachment' together. </p>

<p>'Kammic-retribution' is a moral yet defiled &amp; mundane teaching; based in the ordinary view of 'self'. </p>

<p>'Non-attachment' is a supramundane/transcendent (<em>lokuttara</em>) teaching; based in not-self (<em>anatta</em>). </p>

<p>Please refer to <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.117.than.html" rel="nofollow noreferrer">MN 117</a>, which distinguishes these matters. </p>

<p>This being said, any important &amp; essential relationship in life must be looked after, for example, the relationship an enlightened monk must have with laypeople. </p>

<p>The Buddha taught 'non-attachment' rather than 'detachment'. The advanced Buddhist practitioner learns to have <em>metta</em> without attachment. Having <em>metta</em> will look after/safeguard any relationship. </p>
