Manu Smriti 10.129
शक्तेनापि हि शूद्रेण न कार्यो धनसञ्चयः ।
शूद्रो हि धनमासाद्य ब्राह्मणानेव बाधते ॥ १२९ ॥
"No collection of wealth must be made by a Sudra, even though he be able (to do it); for a Sudra who has acquired wealth, gives pain to Brahmanas."
Here's the explanation given by Medhatithi in his commentary on the Manu Smriti:
‘Even though he is able’—by means of agriculture and such acts,—wealth shall not be amassed by the Śūdra. In support of this the Author adds an argument in the form of a declamatory statement—‘Having acquired wealth the Śūdra harasses the Brāhmaṇas.’ “What is the harassment caused to Brāhmaṇas?” Becoming very rich, they would make the Brāhmaṇas accept gifts from themselves, and the accepting of gifts from the Śūdra has been forbidden for them; hence becoming a party to their doing what is forbidden, he would incur sin. The danger of incurring such sin however could not apply to the case of one who goes on fulfilling all that is prescribed for him. Hence the ‘harassment’ of the Brāhmaṇa that is meant is only this that he would no longer serve them.
So the problem is that by acquiring wealth he may be tempted to stop performing his duty of serving Brahmanas and other members of the first three castes. And so he's forbidden from acquiring wealth in order to prevent this temptation.
However, if a low-caste person violates this and acquires wealth anyway, he should use this wealth to support members of the first three castes, as described in this chapter of the Gautama Dharma Sutras:
And a man of higher caste (who is his master and has fallen into distress must be maintained) by him. His hoard shall serve this purpose.
Sometimes we need to interpret scriptures based on context. The very next verse says the above given duties are duties at the time of distress.
एते चतुर्णां वर्णानामापद्धर्माः प्रकीर्तिताः ।
यान् सम्यगनुतिष्ठन्तो व्रजन्ति परमं गतिम् ॥ १३० ॥
The duties of the four castes (varna) in times of distress have thus been declared, and if they perform them well, they will reach the most blessed state.(130)
Also prohibiting to amass wealth doesn't necessarily mean not allowed to have wealth at all. This means only stockpiling of wealth is prohibited. Even Brahmins are not allowed to stockpile wealth which vaishyas alone can do.
If a Brahmana happens to have more wealth than what is necessary for maintaining himself and his family for three years, he should with that wealth perform sacrifices. A Brahmana should never acquire wealth for nothing.
[Mahabharata Book 13 Chapter 47]
Several other verses in the Manusmriti may indicate that even Shudras can earn money and wealth. In the very same chapter,
विद्या शिल्पं भृतिः सेवा गोरक्ष्यं विपणिः कृषिः । धृतिर्भैक्षं कुसीदं च दश जीवनहेतवः ॥ ११६ ॥
Learning, handicrafts, working on hire, service, cattle-tending, trade, agriculture, contentment, begging and money-lending,—these are the ten means of livelihood.—(116)
Medhātithi writes:
This verse sets forth the means of livelihood for all men, during times of distress.
‘Learning’—here stands for sciences other than the Veda; such, for instance, as Medicine, Logic, Physics, Toxicology and so forth,—all which are not reprehensible, when used as a means of livelihood.
‘Handicraft.’—This has been already explained.
‘Working on hire’—as a servant
‘Service’—acting according to the wishes of another person.
‘Contentment’—This has been added only by way of illustration.
The meaning of this verse is that in the absence of the particular means of livelihood specifically assigned to each caste, these ten means are open to all men.—(116)
Also one more verse:
कृष्णसारस्तु चरति मृगो यत्र स्वभावतः ।स ज्ञेयो यज्ञियो देशो म्लेच्छदेशस्त्वतः परः ॥
एतान्द्विजातयो देशान् संश्रयेरन् प्रयत्नतः ।शूद्रस्तु यस्मिन् कस्मिन् वा निवसेद् वृत्तिकर्शितः ॥ (Manu II.23-24)
But the region where the spotted deer roams by nature is to be known as the ‘land fit for sacrificial acts’; beyond that is the ‘land op the Mlecchas. The twice-born people should seek to resort to these countries; the Śūdra may however, when distressed for a living, reside in any land.
Medatithi writes:
In as much as service of the twice-born people constitutes the prescribed duty of the śūdra, it follows as a matter of course that the latter should reside where the former reside; but if he fails to obtain a living in that country, then he may go. and live in another country; this is what is permitted (in the latter part of the verse). When the man comes to have a large family, or becomes unfit for service,—even though the twice-born person on whom he is dependent may be prepared to support him,—the śūdra may go and live in another country, where there may be a chance for him to acquire wealth.
śaktenāpi hi śūdreṇa na kāryo dhanasañcayaḥ | śūdro hi dhanamāsādya brāhmaṇāneva bādhate||
sakta prowess, capacity; sudra citizens; na karya not thru rituals; dhana+sancayah can accumulate wealth;
It is a common mistake to take the term "shudra" in MS to mean varna. It is used generically to mean "general talent or capacity", where Brahmin, Kshatriya and Vaishya are "specific talents or capacities". Everyone is born shudra (janme jayate shudro...), so the most generic meaning of shudra is "citizen".
A shudra accumulates wealth through personal capacities, not thru the rituals of archana & community service (as in kriya+carya).
In the second line, the term brahmana is taken as "divine knowledge" (not brahmin varna), badhate is to harness.
But wealth alone is insufficient to obtain that which can be harnessed only by divine knowledge.
