UniCARE Financial Corp., Irvine, reported that net income for 1987 rose more than 50%, to $4.9 million, which included a gain on investments of $733,000. Last year's net income was $3.2 million, including $2.1 million in investment gains. Premiums earned totaled $44.7 million, 33% higher than last year's $33.5 million. For the fourth quarter, net income increased 46%, to $1.2 million, contrasted with $840,000 in the year earlier period. Included in those figures are net gains from investments of $60,000 in 1987 and $281,000 in 1986. Premiums earned were $11.5 million, up 14% from the $10.1 million reported a year ago. UniCARE Financial Corp., through its operating subsidiary, UniCARE Insurance Co., primarily writes workers' compensation insurance in California.