Canto 2 -
Ayodhyā-kāṇḍa
Chapter 45: The Brāhmaṇas from Ayodhyā Follow Rāma
Text 2.45.25

हृदयेष्वेव तिष्ठन्ति वेदा ये नः परं धनम्।
वत्स्यन्त्यपि गृहेष्वेव दाराश्चारित्ररक्षिताः॥

hṛdayeṣv eva tiṣṭhanti vedā ye naḥ paraṁ dhanam
vatsyanty api gṛheṣv eva dārāś cāritra-rakṣitāḥ

hṛdayeṣu eva = in our hearts; tiṣṭhanti = stay; vedāḥ = the Vedas; ye = which; naḥ = are our; param = supreme; dhanam = wealth; vatsyanti api = will live; gṛheṣu eva = in our homes; dārāḥ = our wives; cāritra-rakṣitāḥ = protected by good conduct.

The Vedas, which are our supreme wealth, stay in our hearts. Protected by good conduct, our wives will live in our homes.1

This is spoken in anticipation of Lord Rāma’s thought, “How can you abandon the Veda which is the wealth of brāhmaṇas and the protection of your wives who are companions in dharma just to follow us?”1

The brāhmaṇas had memorized the Vedas and [hence] it was in their hearts. They implied that there would be no loss because of them not uttering the Vedic mantras [like they did in their homes on a daily basis].2 Their wives were protected by their good conduct of avowed chastity and service to their husbands. They implied that [the piety of their wives’] excellent character and activities protected themselves and so they were not [actually] protected by their husbands.

They then anticipated that Rāma might tell them, “On My request, please stop [following Me].” With this in mind, they spoke the next verse. 

1]. They imply that they won’t return home without Rāma. They won’t forget the Veda by not participating in their daily recitation of the Vedic texts at their homes because they have already memorized them—these sacred texts were now in their hearts. Their wives didn’t need their protection too—they were protected by their own good conduct. This was what was in their minds

1 Brāhmaṇas are meant to recite the actual texts of Vedic scriptures on a daily basis. To not engage in such daily recitation can easily lead to forgetfulness of those texts, which are in fact, their actual wealth. This is tantamount to abandoning the Vedas.

2 They would not forget them..