This niyamaḥ is used to associate the last word of a compound with all the previous words of a dvandva samāsaḥ. An example is, रामलक्ष्मणपुत्राः गतवन्तः, रामपुत्राः लक्ष्मणपुत्राः गतवन्तः । Here, the word पुत्र is associated with राम and लक्ष्मण । The rule states द्वन्द्वान्ते श्रूयमाणं, however, that would mean within the dvandva compound, the last word. Then how does the word पुत्र associates with राम and लक्ष्मण (रामलक्ष्मणौ, तयोः पुत्राः => तत्पुरुषः समासः) ?

This rule is also used in प्रातिपदिकार्थलिङ्गपरिमाणवचनमात्रे प्रथमा सूत्रम् ।

https://ashtadhyayi.com/sutraani/2/3/46

The core principle is that the word in ending (or starting) of whole compound shall have an association with dvanda. It can be dvandvagarbha XYZ samāsa. In this case, it is dvandvagarbhaḥ tatpuruṣaḥ.

रामश्च लक्ष्मणश्चेति रामलक्ष्मणौ। तयोः (रामलक्ष्मणयोः) पुत्राः इति रामलक्ष्मणपुत्राः।

Such is seen in bahuvrīhi as well.

एकद्वित्रिमात्राः ह्रस्वदीर्घप्लुताः॥१।१।५॥ SHS ¹

एका च द्वे च तिस्रश्चेति एकद्वितिस्रः। एकद्वितिस्रः मात्राः येषां ते एकद्वित्रिमात्राः॥ Here compound is dvandvagarbhaḥ bahuvrīhi.

So, the rule only says about association with pada and not any specific compound. Though, we can think that dvandvagarbhaḥ dvandva wouldn't be possible. We need to find if there are some examples of dvandvagarbhaḥ avyayībhāvaḥ or dvandvagarbhaḥ karmadhārayaḥ.

The full न्यायः is - द्वन्द्वादौ द्वन्द्वमध्ये द्वन्द्वान्ते श्रूयमाणं पदं प्रत्येकमभिसम्बध्यते ।

The following is quoted from Ref 1.

In a द्वन्द्व-गर्भः compound (a compound which contains within it a द्वन्द्वः compound) the पदम् which (immediately) follows the द्वन्द्व: compound connects individually with the members of the द्वन्द्वः compound.

उदाहरणम् –

रागद्वेषवियुक्तैस्तु विषयानिन्द्रियैश्चरन्‌ | आत्मवश्यैर्विधेयात्मा प्रसादमधिगच्छति || गीता 2-64||

First we form the द्वन्द्वः compound रागद्वेषौ as follows – रागश्च द्वेषश्च = रागद्वेषौ – attachment and aversion.

Then we form the द्वन्द्व-गर्भ-तृतीया-तत्पुरुष: compound रागद्वेषवियुक्तानि as follows – रागद्वेषाभ्यां वियुक्तानि = रागद्वेषवियुक्तानि (इन्द्रियाणि) – (senses) devoid of attachment and (devoid of) aversion. The विवक्षा in the verse is तृतीया-बहुवचनम् hence we get the form रागद्वेषवियुक्तैः (इन्द्रियैः)।

As per the न्यायः – द्वन्द्वान्ते श्रूयमाणं पदं प्रत्येकमभिसम्बध्यते, in the final compound ‘रागद्वेषवियुक्त’ the पदम् ‘वियुक्त’ which (immediately) follows the द्वन्द्वः compound ‘रागद्वेष’ connects individually with the members (‘राग’ and ‘द्वेष’) of the द्वन्द्वः compound. Hence we get the meaning ‘devoid of attachment and devoid of aversion.

Quoted from Ref 3. As per the न्याय: – द्वन्द्वान्ते श्रूयमाणं पदं प्रत्येकमभिसम्बध्यते, in the final compound ‘योगवैराग्ययुक्त’ the पदम् ‘युक्त’ which (immediately) follows the द्वन्द्व: compound ‘योगवैराग्य’ connects individually with the members (‘योग’ and ‘वैराग्य’) of the द्वन्द्व: compound. Hence we get the meaning ‘योगवैराग्ययुक्त’ = ‘योगयुक्त’ + ‘वैराग्ययुक्त’ = ‘endowed with Yoga’ and ‘endowed with dispassion.’

References:

2. https://www.nios.ac.in/media/documents/bgp/246_Sanskrit%20Vyakarna_Hindi/246_Sanskrit%20Vyakarna_lesson_5.pdf
3. https://avg-sanskrit.org/2016/05/

Yes. I found this very interesting passage in vyutpattivāda's commentary "Śāstrakalā" where he has shown examples of all three. See highlighted part. For dvandvamadhya, he says: āṅkividhiṇatveṣūpasargatvapratiṣedho vaktavyaḥa.¹